Question

Given the venn diagram below, what is the correct notation!A. G∩(M∪F)′B. (M∩F)′C. none of theseD. (M∪F)′

Answer 1

Explanation:

The image shows a Venn diagram of two sets M and F inside of a containing set G.

We must recall the following notations:

U = Union of sets. Everything inside of any of the sets.

∩ = Intersection between two sets. The common part of both sets.

' = Negation. Everything outside of a set or a set operation.

It's required to express in set notation the grayed part of the diagram. Note it's inside of G and outside of both M and F.

As stated above, the notation to express the union of sets is U and it's precisely the white region of the diagram. So M U F is the white part.

But we want the outside of that white part, so we use (M U F)'.

That is outside of the union, but it includes everything (the entire universe). So we must intercept that with G to take only the grayed part, so the answer is:

A. G∩(M∪F)′

Answer 2

Sets

The image shows a Venn diagram of two sets M and F inside of a containing set G.

We must recall the following notations:

U = Union of sets. Everything inside of any of the sets.

∩ = Intersection between two sets. The common part of both sets.

' = Negation. Everything outside of a set or a set operation.

It's required to express in set notation the grayed part of the diagram. Note it's inside of G and outside of both M and F.

As stated above, the notation to express the union of sets is U and it's precisely the white region of the diagram. So M U F is the white part.

But we want the outside of that white part, so we use (M U F)'.

That is outside of the union, but it includes everything (the entire universe). So we must intercept that with G to take only the grayed part, so the answer is:

A. G∩(M∪F)′