Q. 1

# Mark the correct alternative in the following:

If *A* = {1, 2, 4}, *B* = {2, 4, 5}, *C* = {2, 5}, then (*A*−*B*) × (B − C) is

A. {(1, 2), (1, 5), (2, 5)}

B. {(1, 4}

C. (1, 4)

D. none of these.

Answer :

When we subtract two sets, say (A – B), the result will be a set obtained on removing those elements from A which also exist in B.

Note : We do not consider the elements of the subtracted set(here B) if it is not present in A.

So, we have (A – B) = {1, 2, 4} – {2, 4, 5}

= {1}

Similarly, we have (B - C) = {2, 4, 5} – {2, 5}

= {4}

[When we multiply two sets, each element of first set is paired with every element of other in an ordered pair of form (x, y)

where x belongs to first set and y to the other.]

Now, (*A*−*B*) × (B − C) = {1} × {4}

= {(1, 4)}

Since, it is a set so it is written in curly braces.

Therefore, option B is correct.

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