If set A has 6 elements, A∩B has 3, and A(Union Symbol)B has 9, then set B has______ elements.?

Draw venn diagrams to help with these

A U B has 3 elements, and A has 6 elements, then there are 3 elements in A that are not in B.

Since the union of A and B has 9 elements, and A has 3 elements not in B, then B must have 6 elements in it.

3 in only A, 3 in only B, and 3 in both in this example.

It is still easier to visualize with Venn diagrams, though.

If AUB has 9 elements, and A has 6, then there are 3 elements in B that are not in A.

If A∩B has 3 elements, there are 3 elements in B that are in A.

B in A + B not in A = all of B

3 + 3 = 6

let A be a set diff from B

A and B together,

i.e. elements exclusive to A, plus those in common with B, plus those exclusive to B

make 9 elements

A and B share 3 elements; with A having 6 elements in total, how many elements belong ONLY to A ? 6 -3 = 3

hence, we have 3 + 3 + x = 9 => x = 3 (no. of elements EXCLUSIVE in B)

but wait ... B shares some elements with A

add these up to those exclusive to B and u get : 3 + 3 = 6 (total no. of elements in B)

Side Note: In math jargon, when I say that 2 sets SHARE a no. of elements, I usually talk about INTERESECTION .... and when I TOTAL the no. of elements in the 2 sets, I'm actually referring to their UNION

Wish I could skype you as it is hard to draw the Euler Circles

to put in the informatio.....

.........................A..............AintersectB.................B

........................3.........................3.........................3

...................................................3........... + ..........3 = 6..ANSWER

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A (Four Day Late) CHRISTMAS PRESENT FOR YOU

Ask someone to write a number, say a five-digit number.

(Can be a 2-digit.....3-digit.....4-digit....ect..…

Suppose the number written is

57836

Now, without showing the asker, you write a number on

a sheet of paper and keep it folded. You have to write the

number by subtracting 2 from the above number and

adding 2 in front which will be....

257834

Next, ask the person to write another five-digit number

below his original number. Suppose he writes 37589.

So you now have...

57836

37589

Now you write a five-digit number below it in such a

way that each digit is 9 minus digit above. You now have...

57836

37589

62410

Ask the person to add one more 5-digit number. If he

adds 54732, you add below it 45267. Note that you decided

the number by subtracting each of his digit from 9.

Thus, you now have.....

57836

37589

62410

54732

45267

Next, ask him to add all the number and he gets 257834

Show him the number which you had written as an answer

to this addition earlier in the folded paper and surprise him.

9 = 6 + B - 3

B = 6

A = 6

A∩B = 3

A∪B = 9

A∪B = A + B - A∩B

9 = 6 + B - 3

6 = B