Consider universe positive integer X={1≤n≤8} Proposition P= “n is an even…
2023
Consider universe positive integer X={1≤n≤8} Proposition P= “n is an even integer” Q= “(3 ≤ n ≤ 7) ∧ (n ≠ 6)”
then truth set of P↔Q is
- A.
→ {1,4}
- B.
→ {2,6}
- C.
→ {3,4,5}
- D.
→ {1}
Attempted by 48 students.
Show answer & explanation
Correct answer: A
Universe:
X={1,2,3,4,5,6,7,8}
Given: P: “n is even” ={2,4,6,8}
Q= “(3 ≤ n ≤ 7) ∧ (n ≠ 6)
Numbers from 3 to 7 → {3,4,5,6,7}
Remove 6 →
Q={3,4,5,7}
Biconditional
P↔QP
True when both have same truth value (i.e., both true OR both false)
n | P (even) | Q | P↔Q |
|---|---|---|---|
1 | F | F | T |
2 | T | F | F |
3 | F | T | F |
4 | T | T | T |
5 | F | T | F |
6 | T | F | F |
7 | F | T | F |
8 | T | F | F |
{1,4}
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