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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