Advertisements
Advertisements
Question
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)
Advertisements
Solution
(p → q) ∨ (r ∧ s) ≡ (T → T) ∨ (F ∧ F)
≡ T ∨ F
≡ T
Hence, truth value if T.
APPEARS IN
RELATED QUESTIONS
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) → (r ∧ p)
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Construct the truth table of the following:
p → (q → p)
Construct the truth table of the following:
∼ (∼p ∧ ∼q) ∨ q
Construct the truth table of the following:
[(∼p ∨ q) ∧ (q → r)] → (p → r)
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
Express the following statement in symbolic form.
Mango is a fruit but potato is a vegetable.
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement:
p ↔ ~ q
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q → p
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.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
If proof is lengthy then 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 ∨ r)
Rewrite the following statement without using the connective ‘If ... then’.
If 10 − 3 = 7 then 10 × 3 ≠ 30.
A biconditional statement is the conjunction of two ______ statements.
Find the negation of 10 + 20 = 30
Write the following statements in symbolic form
If Kutab – 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 ______.
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 ______
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
The statement ∼(p ↔ ∼q) is ______.
If a statement b has truth value False and \[(p\wedge q)\leftrightarrow r\] has truth value True, then which of the following has truth value True?
