Chapter 1: Sets

Exercise

Question

Question: 5

10 / 17

Show that if A ⊂ B, then C - B ⊂ C - A.

Answer

1
Prove that every element of set C − B is also an element of set C − A. For this, take any element from set C − B.
Venn diagram showing set A completely inside set B
An element in C − B lies in C but outside B.
Let x $∈$ C - B.
Then x $∈$ C and x $∉$ B.
2
Determine whether x belongs to set A, given that x ∉ B.
Since x $∉$ B and A $⊂$ B, x $∉$ A.
3
Determine whether x is an element of C - A using the information gathered in previous steps.
Venn diagram showing set A completely inside set B
An element belongs to C − A if it lies in C but outside A.
Answer: Since x $∈$ C and x $∉$ A
Therefore, x $∈$ C - A
Hence, C - B $⊂$ C - A
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