Fsc Part 1 Mathematics (Complete Solution)

Q1
Exhibit Aub and A∩B by venn diagrams in the following cases

(i) A ⊆ B

SOLUTION:

If A is a subset of B,then the set A will b contained in B.The shaded region in fig (1) represents (AUB) and the shaded region in fig.2 represents A∩B.

subset

subset

(ii) B⊆A

SOLUTION:

If B is a subset of A,then the set B will b contained in A.The shaded region in fig (a) represents (AUB) and the shaded region in fig.(b) represents A∩B.

subset

subset

(iii) AUA'

SOLUTION:

The whole rectangle in the following figure represents AUA'.

subset

(iv) A and B are disjoint sets.

SOLUTION:

If A and B are disjoint sets,then their union is represented by the shaded region in fig(i).There is no shaded region to represent their intersection in fig(ii).

subset

subset

(v) A and B are overlapping sets

SOLUTION:

If A and B are overlapping sets their union is represented by the shaded region in fig(1).The shaded region in the fig(2) represents the intersection of A and B.

subset

subset

 

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