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WAEC Further Mathematics 2012 Paper

Question : 1

Total: 40

(P \cup Q) \cap (P \cup Q')

Solution:

Concept:

Use the distributive law of set operations and the fact that a set and its complement have no common elements.

Explanation:

Start with the given expression:

(P \cup Q) \cap (P \cup Q')

Apply the distributive law:

(P \cup Q) \cap (P \cup Q') = P \cup (Q \cap Q')

Since

Q \cap Q' = \emptyset

, the expression simplifies to

P \cup \emptyset

Also,

P \cup \emptyset = P

Therefore, the given set is exactly

P

Answer:

P

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