Discrete MathShow that if A \not{\subset} B^{c}, then A \cap B=\phi. Hint



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Discrete Math
Show that if ABc, then AB=ϕ. Hint:Use the contrapositive.

Answer & Explanation



Skilled2021-08-23Added 94 answers

Step 1
Given: ABc
We need to prove that AB=ϕ.
Proof by contradiction:
Suppose ABϕ, then xAB
Therefore xA and xB
Step 2
Since ABc and xA, therefore
xABcxBc. But xB as well. Which is not true because no element of a set B can be found in both B and Bc, as BBc=ϕ. Therefore our assumption that ABϕ must be false.
Hence AB=ϕ.

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