Advertisements
Advertisements
प्रश्न
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
Advertisements
उत्तर
| p | q | (p → q) | [(p → q) ∧ q] | [(p → q) ∧ q]→ p |
| T | T | T | T | T |
| T | F | F | F | T |
| F | T | T | T | F |
| F | F | T | F | T |
APPEARS IN
संबंधित प्रश्न
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.
Construct the truth table of the following statement pattern.
(p ∧ q) ↔ (q ∨ r)
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Construct the truth table of the following:
(∼p ∨ ∼q) ↔ [∼(p ∧ q)]
Construct the truth table of the following:
[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
Express the following statement in symbolic form.
Milk is white or grass is green.
Express the following statement in symbolic form.
I like playing but not singing.
Write the truth value of the following statement.
The Himalayas are the highest mountains but they are part of India in the North East.
Write the negation of the following statement.
− 3 is a natural number.
Write the truth value of the negation of the following statement.
London is in England.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
Write the following statement in symbolic form.
If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.
Find the truth value of the following statement.
It is not true that 3 − 7i is a real number.
If p and q are true and r and s are false, find the truth value of the following compound statement.
p ∧ (q ∧ r)
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q → p
Negation of “some men are animal” is ______.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
3 is prime number if 3 is perfect square number.
Write the negation of the following.
Kanchanganga is in India and Everest is in Nepal.
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 or stocks are not rising iff stocks are rising.
Rewrite the following statement without using the connective ‘If ... then’.
If it rains then the principal declares a holiday.
Consider the following statements.
- If D is dog, then D is very good.
- If D is very good, then D is dog.
- If D is not very good, then D is not a dog.
- If D is not a dog, then D is not very good.
Identify the pairs of statements having the same meaning. Justify.
Negation of p → (p ˅ ∼ q) is ______
If p → q is an implication, then the implication ∼ q → ∼ p is called its
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
If q: There are clouds in the sky then p: it is raining. The symbolic form is ______
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
Which of the following is false?
If p and q are true and rands are false statements, then which of the following is true?
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The inverse of the statement "If its quality is good. then it is expensive.", is ______
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?
Which of the following is logically equivalent to `∼(∼p \implies q)`?
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
Express the following compound statement symbolically:
Delhi is in India but Dhaka is not in Sri Lanka
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
