3.4 SPM Practice (Long Questions)

Question 1:

The Venn diagrams in the answer space shows sets X, Y and Z such that the universal set, $\xi =X\cup Y\cup Z$
On the diagrams in the answer space, shade

$\begin{array}{l}(a)\mathrm{X’}\cap Y,\\ (b)\left(X\cup \mathrm{Y’}\right)\cap Z\end{array}$
 

 Solution:

1. X’ ∩ Y means the intersection of the region outside X with the region Y.
   
2. • Find the region of (X ∪ Y’) first.
   • (X ∪ Y’) means the union of the region X and the region outside Y.
   • The region then intersects with region Z to give the result of  (X ∪ Y’) ∩ Z.
   

Question 2:

The Venn diagrams in the answer space shows sets P, Q and R such that the universal set,
On the diagrams in the answer space, shade

1. Q ∩ R,
2. (P’ ∩ R) ∪ Q.

Solution:

1. Q ∩ R means the intersection of the region Q and the region R.
   
2. • Find the region of (P’ ∩ R) first.
   • (P’ ∩ R) means the region that is outside P and is inside R.
   • The union of this region with region Q give the result of (P’ ∩ R) ∪ Q.