## Monday, 1 October 2012

### Example 7

S(square) is a subset of Q(rectangle).
This is true. A rectangle is defined as having four sides while a square is defined as having four equal sides (both with sides intersecting at 90 degrees). Since the square fulfills a rectangle's criteria but a rectangle does not fulfill a square's criteria, we can say S(square) is a subset of Q(rectangle).

R(rhombuses) is a subset of P(parallelograms).
This is true. A parallelogram is defined as having four sides with opposite sides being parallel while a rhombus is described as having four equal sides with opposite sides being parallel. Since a rhombus fulfills a parallelogram's criteria while a parallelogram fulfills a rhombi's criteria, we can say R(rhombuses) is a subset of P(parallelograms).

T(trapeziums) is not a subset of S, Q, R, P.
A trapezium is a quadrilateral with no sides parallel. Since the rest of the sets are quadrilaterals with parallel lines, we can say T(trapeziums) is not a subset of S, Q, R, P.

Q is a subset of P.
This is true. A parallelogram is a 4-sided shape where opposites sides are parallel. Rectangle fulfills the criteria, hence it is a subset of P. A rectangle's corners must be 90 degrees, and since a parallelogram does not fulfill that criteria, it cannot be a subset of Q.

Therefore, Wai Kit's venn diagram is not right and Mr. Johari's diagram is correct!

However, a square is a rhombus but a rhombus is not a rectangle. So how do we draw a venn diagram in this case? (Mr. Johari please help!)

Done by Carissa Liew