Question

Question #54dde

Answer 1

See a step process below;

Explanation:

The diagram is given below;

From the diagram and in accordance with the details given, we have the following;

`a + b = 15 - - - eqn1`

`a + b + c = 30 - - - eqn2`

Subtracting `eqn1` from `eqn2`, we should have;

`c = 15`

Also;

`n(H ∩ J) rArr 35 = b + 30`

`b = 35 - 30`

`b = 5`

Also;

`n(B) rArr 69 = b + c + 30 + d`

Substituting the values for `b and c`, we should have;

`69 = 5 + 15 + 30 + d`

`69 = 50 + d`

`d = 69 - 50`

`d = 19`

From `eqn1` substitute the value of `b`

`a + b = 15`

`a = 15 - b`

a = 15 - 5#

`a = 10`

Also;

`n(U) rArr a + b + c + d + e + 15 + 30 = 100`

Subsituting the unknown values;

`10 + 5 + 15 + 19 + e + 15 + 30 = 100`

`94 + e = 100`

`e = 100 - 94`

`e = 6`

Therefore;

`a = 10`

`b = 5`

`c = 15`

`d = 19`

`e = 6`

Hope this helps!