Advertisements
Advertisements
प्रश्न
Show that (p ∧ q) ≡ ¬p v ¬q
उत्तर
p | q | p ∧ q | ¬(p v q) | ¬p | ¬q | ¬p v ¬q |
T | T | T | F | F | F | F |
T | F | F | T | F | T | T |
F | T | F | T | T | F | T |
F | F | F | T | T | T | T |
The entries in the columns corresponding to ¬(p ∧ q) and ¬P v ¬q are identical and hence they are equivalent.
APPEARS IN
संबंधित प्रश्न
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
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
Determine the truth value of the following statement.
China is in Europe dr `sqrt(3)` is art integer
Which one of the following sentences is a proposition?
3n ≤ 81, n ∈ N
Which one of the following sentences is a proposition?
How tall this mountain is!
Write the converse, inverse, and contrapositive of the following implication.
If x and y are numbers such that x = y, then x2 = y2
Write the converse, inverse, and contrapositive of the following implication.
If a quadrilateral is a square then it is a rectangle
Construct the truth table for the following statement.
¬(P ∧ ¬q)
Construct the truth table for the following statement
(¬p → r) ∧ (p ↔ q)
Verify whether the following compound propositions are tautologies or contradictions or contingency.
((p v q) ∧¬p) → q
Prove that p → (¬q v r) ≡ ¬p v (¬q v r) using truth table
Choose the correct alternative:
The operation * defined by a * b = `"ab"/7` is not a binary operation on
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 is the contrapositive of the statement (p v q) → r?
Choose the correct alternative:
The truth table for (p ∧ q) v ¬q is given below
p | q | (p ∧ q) v ¬q |
T | T | (a) |
T | F | (b) |
F | T | (c) |
F | F | (d) |
Which one of the following is true?
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