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JAMIA 2023 — Mathematics PYQ

JAMIA | Mathematics | 2023

(𝐴∩𝐵′)∪(𝐴′∩𝐵)∪(𝐴′∩𝐵′) 𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜

Choose the correct answer:

Explanation

Logic

The original expression is:

(A \cap B') \cup (A' \cap B) \cup (A' \cap B')

1. Combine the terms containing $A'$ :

Using the distributive law on the last two parts:

(A' \cap B) \cup (A' \cap B') = A' \cap (B \cup B')

Since $B \cup B'$ is the Universal Set ( $U$ ), and $A' \cap U = A'$ , the expression simplifies to:

(A \cap B') \cup A'

2. Distribute $A'$ over $(A \cap B')$ :

(A \cup A') \cap (B' \cup A')

Since $A \cup A'$ is the Universal Set ( $U$ ):

U \cap (B' \cup A')

3. Final Result:

A' \cup B'