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प्रश्न
Construct the truth table of the following statement pattern.
p → [∼ (q ∧ r)]
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उत्तर
| p | q | r | q ∧ r | ∼ (q ∧ r) | p → [∼ (q ∧ r)] |
| T | T | T | T | F | F |
| T | T | F | F | T | T |
| T | F | T | F | T | T |
| T | F | F | F | T | T |
| F | T | T | T | F | T |
| F | T | F | F | T | T |
| F | F | T | F | T | T |
| F | F | F | F | T | T |
संबंधित प्रश्न
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Write down the following statements in symbolic form :
(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls
Construct the truth table of the following statement pattern.
(p ∧ ∼q) ↔ (p → q)
Construct the truth table of the following statement pattern.
(p ∧ q) ↔ (q ∨ r)
Construct the truth table of the following:
p → (q → p)
Construct the truth table of the following:
(∼p ∨ ∼q) ↔ [∼(p ∧ q)]
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∧ q) is T
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∨ q) → q is F
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p ↔ ~ q
Fill in the blanks :
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q : It is interesting.
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q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p → q
Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
(p ∧ q) ∧ ∼ r
Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
∼ (p ∨ q) ∧ r
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(Hint : p → q ≡ ∼ p ∨ q)
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10 > 5 and 3 < 8
Write the negation of the following statement.
I will have tea or coffee.
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∀ n ∈ N, n + 3 > 9.
If p → q is an implication, then the implication ∼ q → ∼ p is called its
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Find the negation of 10 + 20 = 30
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Write the following statements in symbolic form
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Write the negation of p → q
Negation of “Some men are animal” is ______.
If q: There are clouds in the sky then p: it is raining. The symbolic form is ______
If p and q are true and rands are false statements, then which of the following is true?
Which of the following is NOT true for p → q.
Let S be a non-empty subset of R. Consider the following statement:
p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p?
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Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
Using the statements
p: Seema is fat,
q: Seema is happy,
Write the following statements in symbolic form;
- Seema is thin and happy.
- If Seema is fat then she is unhappy.
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
