Determine whether each of the statement in Exercise for all sets A, B and C, A – (B – C) = (A – B) – C, is true or false. Justify your answer.
Determine whether each of the statement in Exercise for all sets A, B and C, A – (B – C) = (A – B) – C, is true or false. Justify your answer.

Solution:

The statement is false

As per the question,

Three sets are A, B and C

We need to check: A-(B-C)=(A-B)-C is true or false.

Step 1:

NCERT Exemplar Class 11 Maths Chapter 1-6

B-C

Step 2:

NCERT Exemplar Class 11 Maths Chapter 1- 7

A-(B-C)

Step 3:

NCERT Exemplar Class 11 Maths Chapter 1-8

 

A-B

Step 4:

NCERT Exemplar Class 11 Maths Chapter 1-9

(A-B)-C

So now, from the Venn diagrams, we have,

Step 2 and Step 4 are not equal

Hence, A-(B-C) \neq(A-B)-C

As a result, the provided statement “for all sets A, B and C, A-(B-C)=(A-B)-C ” is false.