venn diagram help please

i don’t understand... the apostrophe’s

The apostrophe means 'complement' and in simple terms, A' is the entire region EXCEPT A. So imagine shading in the entire rectangle box but shading around the circle labelled A as to exclude it.

I also recommend you use different coloured pencils (or use different shading pattern with your pen) because then it's much clearer what your region must be.
For instance, in $A \cap B'$ you would shade in A with one colour. Then shade in B' with another colour. Then since we have an 'intersection' $\cap$ then you just need to look where these two colours overlap eachother. Shade in this region with your pen (or otherwise clearly) as your final answer.

oh so i don’t shade in the middle aswell? got it.

yeah i don’t think we’re allowed different colours in the exam. sorry but can you give me an example of a pattern i can use to be clearer? would highly appreciate it

The middle is part of A. So since you ignore A then you automatically ignore the middle when shading in A'.


One common shading pattern would be (and i will use the same example as above) to use //// parallel line pattern to shade in A, then \\\\ parallel line pattern to shade in B'.
Then it's clear where they overlap and intersect.

Anyhow, I know you probably cant use coloured pencils in exams but Im saying you should use them while you're learning this content and once you get a hang of it then you wont need colours anymore.

For the first question, shade the area outside the circles.
For the second question, shade all areas except the A circle without the part in the centre.
For the third question, you only need to shade the A circle without the part in the centre overlapping A and B.
For the question 10, the probability is 44/50

No point giving away answers, especially wrong ones (your sol to second venn diagram shading is wrong) so just give hints instead and they will obtain the answer themselves.

is this okay?


i mean its clear isn’t it?

Not super clear.

Look, shade in the A circle entirely with //// strokes.
Then shade in the entire B' region with \\\\ strokes.

Where do they intersect ?? Fill in this region by a full shading.

oh so i don’t shade in the middle aswell? got it.

yeah i don’t think we’re allowed different colours in the exam. sorry but can you give me an example of a pattern i can use to be clearer? would highly appreciate it

Not super clear.

Look, shade in the A circle entirely with //// strokes.
Then shade in the entire B' region with \\\\ strokes.

Where do they intersect ?? Fill in this region by a full shading.

...

No it's not quite there still.

You are finding $A' \cup B$. So shade in $A'$ first using //// strokes. You get:



Then shade in the $B$ using \\\\ strokes. You get:



And since $A' \cup B$ means EITHER //// OR \\\\ then you can just fully shade in every region that has a stroked line going through. I've used a yellow highlighter on the compuiter but obviously you can just fill it in with your pen instead. You get:




And if the question had wanted $A' \cap B$ instead, then you just shade in where the two lines //// and \\\\ intersect. You get:







As you can see, when you do it properly it's easy to read and not full of scribles. And just to make it very clear to the examiner or whoever it is assessing you on this topic whenever, you can put a key down such as:

(//// shading) = A'

(\\\\ shading) = B

(full shading) = A' U B

Think about B' meaning not in B so A U B' means shade the area in A or not in B.

Most students find it easier to think in words like this.

U means 'or'

upside down U means 'and'

so if it is U then you also shade the region outside the circles?