Advertisements
Advertisements
प्रश्न
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
p ↔ (q → ∼ p)
उत्तर
p ↔ (q → ∼ p) ≡ T ↔ (T → ∼ T)
≡ T ↔ (T → F)
≡ T ↔ F
≡ F
Hence, truth value is F.
APPEARS IN
संबंधित प्रश्न
Write the truth values of the following.
64 is a perfect square and 46 is a prime number.
If p ∧ q is F, p → q is F then the truth values of p and q are ________.
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.
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.
Can you speak in English?
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 :
“His birthday is on 29th February” is not a statement.
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.
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 high and stocks are rising if and only if stock prices are high.
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
(p ∧ q) → ∼ p.
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
∼ (p ∧ q) → ∼ (q ∧ p)
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∀ x ∈ A, x2 + 2 ≥ 5.
State whether the following statement is True or False:
(p ˅ q) ˄ ~ p is a contradiction
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)
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.
If (p ∧ ~ q) → ~ p is false, the truth values of p and q are respectively.
Find the truth value of the following compound statement:
5 + 4 = 9 and 6 × 3 = 12