ITPEC FE Morning April 2023 Question 1

All of A except the centre, plus the part of B and C outside A — mark which of the eight regions each term covers, then shade their union.

The terms cover these regions:

• •A ∩ C: A only, and the part of A shared with B only
• •A ∩ B ∩ C: the part of A shared with C only
• •A ∩ B ∩ C: the part of B and C outside A

The first two terms together are A ∩ (B ∪ C), which is A without the centre A ∩ B ∩ C. The third adds the B-and-C region outside A. The centre, B only and C only stay white.

Answer (d)

Why not others:

• •(a) — shades A outside B, as if the first term were A ∩ B; the part of A shared only with B is left white
• •(b) — shades A without the centre correctly but drops the third term, A ∩ B ∩ C
• •(c) — drops the middle term A ∩ B ∩ C, so the part of A shared only with C is left white

Key rule: Three sets make eight regions; test each region against every term, and factor out a shared set first to cut the work.

Basic Theory · AI-written, may contain errors