Advertisements
Advertisements
Question
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.
Advertisements
Solution
Symbolic form of the given statement is ~ p ∨~q
∴ ~ p ∨~ q ≡ ~ T ∨ ~ T
≡ F ∨ F
≡ F
Hence, truth value is F.
APPEARS IN
RELATED QUESTIONS
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] → p
Construct the truth table of the following statement pattern.
[p → (q → r)] ↔ [(p ∧ q) → r]
Construct the truth table of the following:
(∼p ∨ ∼q) ↔ [∼(p ∧ q)]
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
Express the following statement in symbolic form.
I like playing but not singing.
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
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.
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 ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If Kiran drives the car, then Sameer will walk.
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.
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 statement.
7 is prime number and Tajmahal is in Agra.
Negation of p → (p ˅ ∼ q) is ______
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
Write the negation of p → q
Choose the correct alternative:
A biconditional statement is the conjunction of two ______ statements
Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)

If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
The negation of (p ∨ ∼q) ∧ q is ______
The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______
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 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.
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
