Advertisements
Advertisements
State whether the following statement is True or False:
p ↔ q is false when p and q have different truth values
Options
True
False
Advertisements
Solution
True
APPEARS IN
RELATED QUESTIONS
Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.
Write the following statement in symbolic form and find its truth value:
∀ n ∈ N, n^{2} + n is an even number and n^{2} - n is an odd number.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Please get me breakfast.
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.
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.
x^{2} – 6x – 7 = 0, when x = 7
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.
4 is odd or 1 is prime.
Write the truth values of the following.
5 is a prime number and 7 divides 94.
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:
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:
(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:
(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:
∼ [(∼ 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, x^{2} + 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
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:
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:
cos^{2}θ − sin^{2}θ = cos2θ for all θ∈R.
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:
`sqrt5` is an irrational but `3sqrt5` is a complex number.
Write the truth value of the following statement:
∀ n ∈ N, n^{2} + n is even number while n^{2} – n is an odd number.
Write the truth value of the following statement:
∃ n ∈ N such that n + 5 > 10.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Every real number is a complex number.
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.
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.
Can you speak in English?
Choose the correct alternative :
Which of the following is not a statement?
Choose the correct alternative :
Which of the following is an open statement?
Which of the following statements is false?
Choose the correct alternative :
For the following three statements
p : 2 is an even number.
q : 2 is a prime number.
r : Sum of two prime numbers is always even.
Then, the symbolic statement (p ∧ q) → ∼ r means.
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 :
Conditional p → q is equivalent to
Choose the correct alternative :
Negation of the statement “This is false or That is true” is
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.
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 :
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 :
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.
x + 3 = 8 ; x is variable.
Solve the following :
State which of the following sentences are statements in logic.
Read a lot to improve your writing skill.
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} = a^{2} + 2ab + b^{2} for all a, b ∈ R.
Solve the following :
State which of the following sentences are statements in logic.
(2 + 1)^{2} = 9.
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.
Do not come inside the room.
Solve the following :
State which of the following sentences are statements in logic.
What a horrible sight it was!
Which of the following sentence is a statement? In case of a statement, write down the truth value.
Every parallelogram is a rhombus.
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.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
If stock prices are high then stocks are not rising.
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∀ x ∈ A, x^{2} < 18.
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∀ x ∈ A, x^{2} + 2 ≥ 5.
Which of the following statement is true
If p is any statement then ( p ˅ ∼ p) is a
State the truth value of `sqrt(3)` is not an irrational number
State the truth Value of x^{2} = 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 ∧ ~r) ∧ (~q ∨ s)
Choose the correct alternative :
Which of the following statement is true?
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:
p ˅ ~ p ≡ ~ c
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 ______
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)`.
Find the truth value of the following compound statement:
5 + 4 = 9 and 6 × 3 = 12