Choose the correct alternative : Negation of the statement “This is false or That is true” is - Mathematics and Statistics

Advertisements
Advertisements
MCQ

Choose the correct alternative :

Negation of the statement “This is false or That is true” is

Options

  • That is true or This is false

  • That is true and This is false

  • That is true and That is false

  • That is false and That is true

Advertisements

Solution

That is true and That is false.

  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 30]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 1.14 | Page 30

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Write truth values of the following statements: ∃ n ∈ N such that n + 5 > 10.


Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.


If p, q, r are the statements with truth values T, F, T, respectively then find the truth value of (r ∧ q) ↔ ∼ p


State which of the following is the statement. Justify. In case of a statement, state its truth value.

5 + 4 = 13


State which of the following is the statement. Justify. In case of a statement, state its truth value.

Congruent triangles are similar.


State which of the following is the statement. Justify. In case of a statement, state its truth value.

x2 = x


State which of the following is the statement. Justify. In case of a statement, state its truth value.

Do you like Mathematics?


State which of the following is the statement. Justify. In case of a statement, state its truth value.

The sunsets in the west


State which of the following is the statement. Justify. In case of a statement, state its truth value.

All real numbers are whole numbers.


State which of the following is the statement. Justify. In case of a statement, state its truth value.

Can you speak in Marathi?


State which of the following is the statement. Justify. In case of a statement, state its truth value.

x2 – 6x – 7 = 0, when x = 7


State which of the following is the statement. Justify. In case of a statement, state its truth value.

The sum of cube roots of unity is zero.


State which of the following is the statement. Justify. In case of a statement, state its truth value.

It rains heavily.


Write the truth values of the following.

64 is a perfect square and 46 is a prime number.


Write the truth values of the following.

5 is a prime number and 7 divides 94.


Write the truth value of the following.

If 3 × 5 = 8 then 3 + 5 = 15.


Write the truth value of the following.

Milk is white if and only if sky is blue.


Write the truth values of the following.

24 is a composite number or 17 is a prime number.


If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(q ∧ r) ∨ (∼ p ∧ s)


If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(p → q) ∧ ∼ r


If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(∼ r ↔ p) → ∼ q


If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

[(∼ p ∧ q) ∧ ∼ r] ∨ [(q → p) → (∼ s ∨ r)]


If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

∼ [(∼ p ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)


If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∃ x ∈ A such that x – 8 = 1


If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, x2 + x is an even number


If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∃ x ∈ A such that x2 < 0


If p ∧ q is F, p → q is F then the truth values of p and q are ________.


Select and write the correct answer from the given alternative of the following question:

If A = {1, 2, 3, 4, 5} then which of the following is not true?


Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

4! = 24.


Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

π is an irrational number.


Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

Please get me a glass of water.


Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

If x is a whole number then x + 6 = 0.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

`sqrt(-4)` is an irrational number.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

He is an actor.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

Two co-planar lines are either parallel or intersecting.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

Bring the motor car here.


Which of the following statements is false?


Choose the correct alternative :

If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is


The negation of the proposition “If 2 is prime, then 3 is odd”, is ______ 


Choose the correct alternative :

The statement (∼ p ∧ q) ∨∼ q is


Choose the correct alternative :

∼ (p ∨ q) ∨ (∼ p ∧ q) is logically equivalent to


Choose the correct alternative :

If p is the sentence ‘This statement is false’ then


Fill in the blanks :

The statement q → p is called as the ––––––––– of the statement p → q.


Fill in the blanks :

If p ∨ q is true then truth value of ∼ p ∨ ∼ q is –––––––––.


Fill in the blanks :

p ↔ q is false when p and q have ––––––––– truth values.


Fill in the blanks :

Truth value of 2 + 3 = 5 if and only if − 3 > − 9 is –––––––––.


State whether the following statement is True or False :

Truth value of 2 + 3 < 6 is F.


State whether the following statement is True or False :

Dual of (p ∧ ∼ q) ∨ t is (p ∨ ∼ q) ∨ C.


State whether the following statement is True or False :

Dual of “John and Ayub went to the forest” is “John and Ayub went to the forest”.


State whether the following statement is True or False :

x2 = 25 is true statement.


State whether the following statement is True or False :

Truth value of `sqrt(5)` is not an irrational number is T.


State whether the following statement is True or False :

p ∧ t = p.


Solve the following :

State which of the following sentences are statements in logic.
Ice cream Sundaes are my favourite.


Solve the following :

State which of the following sentences are statements in logic.
z is a positive number.


Solve the following :

State which of the following sentences are statements in logic.
(a + b)2 = a2 + 2ab + b2 for all a, b ∈ R.


Solve the following :

State which of the following sentences are statements in logic.
Why are you sad?


Solve the following :

State which of the following sentences are statements in logic.
How beautiful the flower is!


Solve the following :

State which of the following sentences are statements in logic.
The square of any odd number is even.


Solve the following :

State which of the following sentences are statements in logic.
All integers are natural numbers.


Solve the following :

State which of the following sentences are statements in logic.
If x is real number then x2 ≥ 0.


Solve the following :

State which of the following sentences are statements in logic.
Do not come inside the room.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

The square of every real number is positive.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

a2 − b2 = (a + b) (a − b) for all a, b ∈ R.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

Please carry out my instruction.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

The Himalayas is the highest mountain range.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

0! = 1


Determine the truth value of the following statement.

It is not true that 2 + 3 = 6 or 12 + 3 =5


Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.

Stock prices are not high or stocks are rising.


If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.

(p ∧ ∼ q) ∨ (∼ p ∧ q)


If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.

∃ x ∈ A, such that x + 3 < 11.


Choose the correct alternative :

Which of the following is not a statement?


The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.


State whether the following statement is True or False:

p → q is equivalent to p → ~ q


State whether the following statement is True or False:

(p ˅ q) ˄ ~ p is a contradiction


State whether the following statement is True or False:

The dual of (p ˄ q) ˅ ~ q is (p ˅ q) ˄ ~ q


State whether the following statement is True or False:

Mathematical identities are true statements


The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______


Without using truth table show that

(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)


If p ↔ q and p → q both are true, then find truth values of the following with the help of activity

p ˅ q

p ↔ q and p → q both are true if p and q has truth value `square`, `square` or `square`, `square`.

p ˅ q

i. If both p and q are true, then p ˅ q = `square` ˅ `square` = `square`

ii. If both p and q are false, then p ˅ q = `square` ˅ `square` = `square`


If p ↔ q and p → q both are true, then find truth values of the following with the help of activity

p ˄ q

p ↔ q and p → q both are true if p and q has truth value `square`, `square` or `square`, `square`

p ˄ q

i. If both p and q are true, then p ˄ q = `square` ˄ `square` = `square`

ii. If both p and q are false, then p ˄ q = `square` ˄ `square` = `square`


Which of the following quantified statement is true?


Let a: ~ (p ∧ ~ r) v (~ q v s) and

b: (p v s) ↔ (q ∧ r).

If the truth values of p and q are true and that of rands are false, then the truth values of a and bare respectively.


The negation of 'For every real number x, `x^2 ≥ 0`' is ______ 


If (p ∧ ~ q) → ~ p is false, the truth values of p and q are respectively.


If the truth value of statement (q ∧ ~ r) → p is false (F), then the truth values of the statements p, q, rare respectively.


If p ↔ (~ p → q) is false, then the truth values of p and q are respectively ______.


If q Λ ∼p is T, then which of the following is correct?


If truth values of p ↔ r, r, p ↔ q are F, T, F respectively, then respective truth values of p and q are ______.


If p `rightarrow` (p ∧ ∼q) is false, then the truth values of p and q are respectively ______.


Consider the following two statements.

Statement p:

The value of sin 120° can be divided by taking θ = 240° in the equation 2 sin `θ/2` = `sqrt(1 + sin θ) - sqrt(1 - sinθ)`.

Statement q:

The angles A, B, C and D of any quadrilateral ABCD satisfy the equation `cos(1/2(A + C)) + cos(1/2(B + D))` = 0

Then the truth values of p and q are respectively.


If p : Every square is a rectangle. q : Every rhombus is a kite, then truth values of p `rightarrow` q and p `leftrightarrow` q are ______ and ______ respectively.


Find the truth value of the following compound statement:

5 + 4 = 9 and 6 × 3 = 12


Share
Notifications



      Forgot password?
Use app×