Question

If B subset of C, is it true that A-B=A-C ? is this result true when difference is replaced by
symmetric difference? Give reason.
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Answer 1

Answer:

The symmetric difference using Venn diagram of two subsets A and B is a sub set of U, denoted by A △ B and is defined by

A △ B = (A – B) ∪ (B – A)

Let A and B are two sets. The symmetric difference of two sets A and B is the set (A – B) ∪ (B – A) and is denoted by A △ B.

Thus, A △ B = (A – B) ∪ (B – A) = {x : x ∉ A ∩ B}

or, A △ B = {x : [x ∈ A and x ∉ B] or [x ∈ B and x ∉ A]}

Symmetric Difference using Venn Diagram

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The shaded part of the given Venn diagram represents A △ B