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0606 P22 - Nov 2019 - Q1 - 3 marks
8365
On each of the Venn diagrams, shade the indicated region.
(i) \((A'\cap B)\cup(A\cap B')\)
(ii) \((A\cap B)\cup C\)
(iii) \(A\cap B\cap C'\)
Solution
Answer: (i) shade the two non-overlapping parts of \(A\) and \(B\); (ii) shade all of \(C\) and the overlap \(A\cap B\); (iii) shade the part common to \(A\) and \(B\) but outside \(C\).
(i) The expression \((A'\cap B)\cup(A\cap B')\) means elements in \(B\) but not \(A\), together with elements in \(A\) but not \(B\). So shade the two outer crescent regions of \(A\) and \(B\), leaving the overlap unshaded.
(ii) The expression \((A\cap B)\cup C\) means everything in \(C\), together with the overlap of \(A\) and \(B\). So shade the whole of \(C\), and also shade any part of \(A\cap B\) which lies outside \(C\).
(iii) The expression \(A\cap B\cap C'\) means elements that are in both \(A\) and \(B\), but not in \(C\). So shade only the part of the overlap \(A\cap B\) which lies outside \(C\).
