Question

A intersection (B-C)=(A intersection B)-C​

Answer 1

Answer:

How do you prove that A intersection (B-C) = (A intersection B)-(A intersection C)?

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How do you prove that A intersection (B-C) = (A intersection B)-(A intersection C)?

Two sets are equal if both are subsets of each other.

Let x∈A∩(B−C).

⇒x∈A and x∈(B−C)⇒x∈B and x∉C.

⇒x∈A∩B and x∉A∩C⇒x∈A∩B−A∩C.

⇒A∩(B−C)⊂A∩B−A∩C.

Let x∈A∩B−A∩C.

⇒x∈A∩B and x∉A∩C.

⇒x∈A,x∈B and x∉C.

⇒x∈A and x∈B−C.

⇒x∈A∩(B−C).

⇒A∩B−A∩C⊂A∩(B−C).

⇒A∩(B−C)=A∩B−A∩C.

Answer 2

Step-by-step explanation:

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