Respuesta :
Answer: (a), (c) and (d) are TRUE and (b) is FALSE.
Step-by-step explanation: Given that A and B are sets in some universal set U.
We are to select the true and false statements from the following :
a) (A – B) is a subset of A.
b) (A – B) is a subset of B.
c) The complement of the complement of A is equal to A.
d) A ∪ (B-A) = A ∪ B.
(a) We know that (A - B) contains all those elements of U which are present in A but not present In B.
So, it will be a subset of set A, not B. The given statement is TRUE.
(b) (A - B) will be a subset of A, not B. The given statement is FALSE.
(c) Since A complement contains those elements of U which are not present in A, so the complement of A complement contains all those elements of U which are not present in A complement.
Therefore, the complement of A complement contains all elements of U which are present in A.
So, the given statement is TRUE.
(d) We know that
(B - A) contains all elements that are present in B, but not A. So, the union of A and (B - A) contains all elements that are present in A and B both.
That is, A ∪ (B-A) = A ∪ B.
The given statement is TRUE.
