Advertisements
Advertisements
Question
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
∼ [(p → q) ↔ (p ∧ ∼ q)]
Solution
∼[(p → q) ↔ (p ∧ ∼q)] ≡ ∼ [(T → T) ↔ (T ∧ ∼ T)]
≡ ~[T ↔ (T ∧ F)]
≡ ~(T ↔ F)
≡ ~ F
≡ T
Hence, truth value is T.
APPEARS IN
RELATED QUESTIONS
Write the following statement in symbolic form and find its truth value:
∀ n ∈ N, n2 + n is an even number and n2 - n is an odd number.
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.
Do you like Mathematics?
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.
x2 – 6x – 7 = 0, when x = 7
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
1 is a prime number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Give me a compass box.
Choose the correct alternative:
Which of the following is always true?
Fill in the blanks :
The statement q → p is called as the ––––––––– of the statement p → q.
State whether the following statement is True or False :
There are 24 months in year is a statement.
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.
All integers are natural numbers.
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?
Determine the truth value of the following statement.
It is not true that 2 + 3 = 6 or 12 + 3 =5
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
(p ∧ q) → ∼ p.
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)
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
