ITPEC IP October 2023 Question 4

(not A) and (B or C) — the shading covers all of B and C, overlap included, but nothing inside A.

Build the condition in two steps:

• •Everything shaded lies in B or in C, and all of both circles outside A is shaded, including the part where B and C overlap: that is B or C
• •Every part of B and C that also lies inside A (A and B, A and C, and the centre shared by all three) is left white, and so is A's own area: AND the union with not A

Answer (b)

Why not others:

• •(a) — B and C keeps only the lens where B and C overlap outside A; the parts of B alone and C alone are shaded too
• •(c) — OR with not A takes in everything outside A, including the unshaded area outside all three circles, and adds the centre inside A through B and C
• •(d) — covers everything except the part of A lying outside B and C, so it shades the area outside the circles and the overlaps with A

Key rule: Shading that spans two sets is OR; cutting a set out of it is AND with NOT. An OR with a negated set brings in the whole outside of that set.

Basic Theory · AI-written, may contain errors