Advertisements
Advertisements
प्रश्न
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
Advertisements
उत्तर
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| p | q | p ↔ q | ~p | ~q | p ∧ q | ~p ∧ ~q | (p ∧ q) ∨(~p∧~q) |
| T | T | T | F | F | T | F | T |
| T | F | F | F | T | F | F | F |
| F | T | F | T | F | F | F | F |
| F | F | T | T | T | F | T | T |
The entries in columns 3 and 8 are identical.
p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
Notes
[1 mark each for column 3 and column 8]
APPEARS IN
संबंधित प्रश्न
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
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) ∧ q] → p
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
Construct the truth table of the following statement pattern.
(q → p) ∨ (∼ p ↔ q)
Write the negation of the following statement.
All men are animals.
Write the negation of the following statement.
− 3 is a natural number.
Write the following statement in symbolic form.
It is not true that “i” is a real number.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
Find the truth value of the following statement.
3 is a prime number and an odd number.
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.
Sunday is not holiday or Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q → p
Fill in the blanks :
Conjunction of two statement p and q is symbolically written as ______.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
To be brave is necessary and sufficient condition to climb the Mount Everest.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
x3 + y3 = (x + y)3 if xy = 0.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The drug is effective though it has side effects.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that Ram is tall and handsome.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
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
Write the negation of the following.
Ramesh is intelligent and he is hard working.
Write the negation of the following.
An angle is a right angle if and only if it is of measure 90°.
Rewrite the following statement without using the connective ‘If ... then’.
If a quadrilateral is rhombus then it is not a square.
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.
Write the negation of the following statement.
10 > 5 and 3 < 8
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Choose the correct alternative:
A biconditional statement is the conjunction of two ______ statements
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 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.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.
Which of the following is logically equivalent to `∼(∼p \implies q)`?
Write the negation of p ↔ q.
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
