# Math Help - Venn Diagram - Determining a logical expression.

1. ## Venn Diagram - Determining a logical expression.

Good evening, folks.

I require help with a venn diagram. I missed a lecture in my studies and I'm wondering if anyone online with more knowledge could provide me with a solution to the following question.

Firstly, Could someone please explain what the logical expression would be for the venn diagram below. Secondly, If i was to also shade x, what would the logical expression become?

If anyone is kind enough to provide me with these solutions could they also explain how the solution was reached.

Many thanks, It's a shame i've only came across this forum today. Maths has been troubling me for a good ten years now!

2. Originally Posted by garethbhs
Good evening, folks.

I require help with a venn diagram. I missed a lecture in my studies and I'm wondering if anyone online with more knowledge could provide me with a solution to the following question.

Firstly, Could someone please explain what the logical expression would be for the venn diagram below. Secondly, If i was to also shade x, what would the logical expression become?

If anyone is kind enough to provide me with these solutions could they also explain how the solution was reached.

Many thanks, It's a shame i've only came across this forum today. Maths has been troubling me for a good ten years now!

The bit in the centre is $A\cap B \cap C$ the other shaded piece of $A$ is $(A\backslash B)\backslash C$ so the combined shaded area is:
$(A\cap B \cap C) \cup ((A\backslash B)\backslash C)$