State whether the following statement is True or False: p ˅ ~ p ≡ ~ c - Mathematics and Statistics

Advertisements
Advertisements
MCQ
True or False

State whether the following statement is True or False:

p ˅ ~ p ≡ ~ c

Options

  • True

  • False

Advertisements

Solution

True

  Is there an error in this question or solution?
Chapter 1.1: Mathematical Logic - Q.2

RELATED QUESTIONS

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


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

x – 3 = 14


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.

A quadratic equation cannot have more than two roots.


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.


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 → s)


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 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 3x + 8 > 40


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

∀ x ∈ A, 2x + 9 > 14


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:

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.


Write the truth value of the following statement:

∀ n ∈ N, n2 + n is even number while n2 – n is an odd number.


Write the truth value of the following statement:

In ΔABC if all sides are equal then its all angles are equal.


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

The sum of interior angles of a triangle is 180°


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

x2 − 6x + 8 = 0 implies x = −4 or x = −2.


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

3 + 5 > 11


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

The number π 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.

x2 - y2 = (x + y)(x - y) for all x, y ∈ R.


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.


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

It may rain today.


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

If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.


Which of the following statements is false?


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:

Which of the following is always true?


Choose the correct alternative :

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


Choose the correct alternative :

If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is


Choose the correct alternative :

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


Choose the correct alternative :

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


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 :

Truth value of if x = 2, then x2 = − 4 is –––––––––.


Fill in the blanks :

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


Fill in the blanks :

Let p : the problem is easy. r : It is not challenging then verbal form of ∼ p → r is –––––––––.


State whether the following statement is True or False :

There are 24 months in year is a statement.


State whether the following statement is True or False :

p ∨ q has truth value F is both p and q has truth value 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 :

“His birthday is on 29th February” is not a statement.


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.
x + 3 = 8 ; x is variable.


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.
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.


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.

Please carry out my instruction.


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

What are the causes of rural unemployment?


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

0! = 1


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

The quadratic equation ax2 + bx + c = 0 (a ≠ 0) always has two real roots.


Determine the truth value of the following statement.

x + y = 0 is the equation of a straight line if and only if y2 = 4x is the equation of the parabola.


Which of the following statement is true


State the truth value of `sqrt(3)` is not an irrational number


State the truth Value of x2 = 25


State the truth value of (p ˅ ∼p)


If statements p, q are true and r, s are false, determine the truth values of the following.

~ p ∧ (q ∨ ~ r)


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


State whether the following statement is True or False:

p ↔ q is false when p and q have different truth values


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 negation of “London is in England” is ______


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


Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).


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`


Given following statements
p: 9 × 5 = 45
q: Pune is in Maharashtra
r: 3 is the smallest prime number

Write truth values by activity

i) (p ˄ q) ˄ r = `(square` ˄ `square)` ˄ `square`

= `square` ˄ `square`

= `square`

ii) ~ ( p ˄ r ) = `~(square` ˄ `square)`

= `~ square`

= `square`

iii) 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.


The position vector of points A and B are `6bar(a) + 2bar(b) and bar(a) -3bar(b)` . If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is 3`bar(a)- bar(b)`.


lf p, q are true statements and r, s are false statements, then find the truth value of ∼ (p ∧ ∼r) ∨ (∼q ∨ s).


Using truth table prove that:

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`


Share
Notifications



      Forgot password?
Use app×