Advertisements
Advertisements
Question
Choose the correct alternative:
Which one of the following is not true?
Options
Negation of a statement is the statement itself
If the last column of the truth table contains only T then it is a tautology
If the last column of its truth table contains only F then it is a contradiction
If p and q are any two statements then p ⟷ q is a tautology
Solution
If p and q are any two statements then p ⟷ q is a tautology
APPEARS IN
RELATED QUESTIONS
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
¬ P
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
p → ¬q
Write the following sentences in symbolic form using statement variables p and q.
19 is a prime number or all the angles of a triangle are not equal
Write the following sentences in symbolic form using statement variables p and q.
19 is a prime number and all the angles of a triangle are equal
Write the following sentences in symbolic form using statement variables p and q.
19 is not a prime number
Determine the truth value of the following statement.
If 6 + 2 = 5, then the milk is white.
Which one of the following sentences is a proposition?
Peacock is our national bird
Construct the truth table for the following statement.
¬P ∧ ¬q
Show that (p ∧ q) ≡ ¬p v ¬q
Show that ¬(p → q) ≡ p ∧¬q
Prove that q → p ≡ ¬p → ¬q
Prove p → (q → r) ≡ (p ∧ q) → r without using the truth table
Prove that p → (¬q v r) ≡ ¬p v (¬q v r) using truth table
Choose the correct alternative:
Which one of the following statements has the truth value T?
Choose the correct alternative:
If a compound statement involves 3 simple statements, then the number of rows in the truth table is
Choose the correct alternative:
Which one is the inverse of the statement (p v q) → (p ∧ q)?
Choose the correct alternative:
Which one of the following is incorrect? For any two propositions p and q, we have
Choose the correct alternative:
The dual of ¬(p v q) v [p v(p ∧ ¬r)] is
Choose the correct alternative:
The proposition p∧(¬p∨q)] is
Choose the correct alternative:
Determine the truth value of each of the following statements:
(a) 4 + 2 = 5 and 6 + 3 = 9
(b) 3 + 2 = 5 and 6 + 1 = 7
(c) 4 + 5 = 9 and 1 + 2 = 4
(d) 3 + 2 = 5 and 4 + 7 = 11