Question

If a= -35,b= 10 and c= -5, verify that a×(b+c)=a×b+a×c​

Answer 1

Answer:

This question was previously asked here: For all sets A,B, and C, If B ∩ C ⊆ A, then (A-B) ∩ (A-C) ≠∅

However, it didn't help me much so I wanted if someone could verify my working and correct me where I am wrong.

My initial question is: For all sets A, B and C, if (B∩C)⊆A, then (A−B)∩(A−C)≠∅

I know this is true by drawing a Venn Diagram.

Proof: (B∩C)⊆A

x∈(B∩C)⇒x∈A

x∈(B∩C)c∩A

x∈A∩(Bc∩Cc)

x∈(A∩Bc)∩(A∩Cc)

Which is (A−B)∩(A−C)≠∅

Thank you for any help.