Advertisements
Advertisements
प्रश्न
Which of the following statements is false?
विकल्प
`p ∧ (∼ p)` is contradiction
`(p → q) ↔ (∼ q → ∼ p)` is a contradiction
`~ (∼ p) ↔ p` is a tautology
`[(p → q) ∧ (∼ q)] → (∼ p)` is a tautology
उत्तर
`bb((p → q) ↔ (∼ q → ∼ p))` is a contradiction
APPEARS IN
संबंधित प्रश्न
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.
It rains heavily.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Please grant me a loan.
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
Fill in the blanks :
The statement q → p is called as the ––––––––– of the statement p → q.
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.
0! = 1
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
∼ (p ∧ q) → ∼ (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 ∧ ~r) ∧ (~q ∨ s)
Choose the correct alternative :
Which of the following statement is true?
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:
p ˅ ~ p ≡ ~ c
Without using truth table show that
(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)
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?
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.