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I'm trying to disprove both and so far I was able to disprove part b as shown

A. If A − C = B − C then A = B A = B = C = B. If A ∩ C = B ∩ C then A = B A = {1,2,3} B = {1,2,3,4} C = {1} With the def of ∩, A ∩ C share and element 1 as for B ∩ C also share a element of 1 but A does not equal B.

I'm stuck on finding an example to disprove A, or would it be easier to disprove it by using definitions and logical equivalences?

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    let $c=\{4\}$ and use $A,B$ from case B – 2017-02-10

3 Answers 3

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You are correct in that you only need to come up with a counter example to disprove a statement. You can modify the sets you have in part b for part a. Just let $$ B= \{2,3 \}$$

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    so from my understanding, if C has an element that is not in B, it is still left with B = {2, 3} for B - C – 2017-02-10
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    Correct, if B and C do not share any elements then B-C = B – 2017-02-10
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One of $A$ or $B$ could contain more points of $C$ than the other.. After removal of those they could be the same.

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Let RED=A, ORANGE=B, CYAN=C.

Then:

set counterexamples

The first fails case A, the second fails case B.