Advertisements
Advertisements
प्रश्न
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Advertisements
उत्तर
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| p | q | r | p∧q | (p∧q)→r | q→r | p→(q→r) |
| T | T | T | T | T | T | T |
| T | T | F | T | F | F | F |
| T | F | T | F | T | T | T |
| T | F | F | F | T | T | T |
| F | T | T | F | T | T | T |
| F | T | F | F | T | F | T |
| F | F | T | F | T | T | T |
| F | F | F | F | T | T |
T |
The entries in columns 5 and 7 are identical.
∴ (p ∧ q) → r ≡ p → (q → r).
APPEARS IN
संबंधित प्रश्न
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p
Write the following compound statement symbolically.
If ΔABC is right-angled at B, then m∠A + m∠C = 90°.
Construct the truth table of the following statement pattern.
(p ∧ ∼q) ↔ (p → q)
Construct the truth table of the following statement pattern.
p → [∼ (q ∧ r)]
Construct the truth table of the following:
p → (q → p)
Express the following statement in symbolic form.
Mango is a fruit but potato is a vegetable.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra
Write the negation of the following statement.
2 + 3 ≠ 5
Write the truth value of the negation of the following statement.
For every x ∈ N, x + 3 < 8.
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
If p and q are true and r and s are false, find the truth value of the following compound statement.
(p → q) ∨ (r ∧ s)
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
If Sunday is not holiday then Ram studies on holiday.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The Sun has set and Moon has risen.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If a real number is not rational, then it must be irrational.
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 → r
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If price increases, then demand falls.
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Write the negation of the following.
Ramesh is intelligent and he is hard working.
Write the negation of the following.
If x ∈ A ∩ B, then x ∈ A and x ∈ B.
Write the negation of the following statement.
10 > 5 and 3 < 8
Write the negation of the following statement.
I will have tea or coffee.
A biconditional statement is the conjunction of two ______ statements.
Find the negation of 10 + 20 = 30
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
Write the following statement in symbolic form:
Milk is white if and only if the sky is not blue.
Write the following statements in symbolic form
If Kutab – Minar is in Delhi then Taj - Mahal is in Agra
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
Negation of “Some men are animal” is ______.
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 p and q are true and rands are false statements, then which of the following is true?
The inverse of the statement "If its quality is good. then it is expensive.", is ______
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______
Conditional of p → q is equivalent to p → ∼ q.
Which of the following is logically equivalent to `∼(∼p \implies q)`?
If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
If p, q are true statements and r, s are false statements, then write the truth value of the compound statement
(p `→` ∼ r) `→` (q ∧ s)
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
