Consider the statement, \"if A is a subset of B and C is any set, then A\\C is a

Question

Consider the statement, "if A is a subset of B and C is any set, then AC is a subset of BC."

The lines below form a supposed proof of this statement. Select the first line that is either incorrect or does not follow from the lines above it. If the proof is correct, select the last option.

Options:

Assume that A is a subset of B.

Suppose x is in A. Then x is in B. Since x is in B, then x is not in C.

Hence, x is in B C.

Hence, A C is a subest of B C.

Assume that A is a subset of B.

Suppose x is in A. Then x is in B. Since x is in B, then x is not in C.

Hence, x is in B C.

Hence, A C is a subest of B C.

Explanation / Answer

Line 2 is incorrect because C is any set therefore it may or may not be disjoint with B.so ,we can't conclude that since x is in B ,then it can't be in C

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