Advertisements
Advertisements
Question
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∧ q) is T
Advertisements
Solution
| p | q | p ∨ q | p ∧ q |
| T | T | T | T |
| T | F | T | F |
| F | T | T | F |
| F | F | F | F |
Since p ∨ q and p ∧ q both are T, from the table, the truth values of both p and q are T.
APPEARS IN
RELATED QUESTIONS
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
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.
The angle is right angle if and only if it is of measure 90°.
Construct the truth table of the following statement pattern.
[(p → q) ∧ q] → p
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) ∨ q
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
Write the following statement in symbolic form.
It is not true that “i” is a real number.
Find the truth value of the following statement.
If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.
Find the truth value of the following statement.
3 is a prime number and an odd number.
If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
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.
Mona likes Mathematics and Physics.
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.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is not true that the proof is lengthy but it is interesting.
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
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)
Write the negation of the following.
Kanchanganga is in India and Everest is in Nepal.
Rewrite the following statement without using the connective ‘If ... then’.
If a quadrilateral is rhombus then it is not a square.
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
Write the negation of the following statement.
∀ n ∈ N, n + 3 > 9.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
Negation of p → (p ˅ ∼ q) is ______
A biconditional statement is the conjunction of two ______ statements.
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
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
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)
If q: There are clouds in the sky then p: it is raining. The symbolic form is ______
Which of the following is false?
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
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?
The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
The statement ∼(p ↔ ∼q) is ______.
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)
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
