How to use a Venn Diagram

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ISEE Middle Level Quantitative Reasoning › How to use a Venn Diagram

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Venn_3

Define:

Universal set $U =\mathbb{N}$ , the set of all natural numbers.

= { | is a multiple of 3}

= { | is a multiple of 5}

If all of the natural numbers were to be placed in their appropriate places in the above Venn diagram, which of the following would be placed in the gray region?

CORRECT

Explanation

The gray region is the region outside both and and is therefore the set of natural numbers that are multiples of neither 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3: $7,431 \div 3 = 2,477$ and $3,966 \div 3 = 1,322$ .

7,916 is not divisible by 5 as it ends in 6; it is not divisible by 3 as $7,916 \div 3 =2,638 ; R; 2$ . Therefore, it is the correct choice.

Venn_3

Define:

Universal set $U =\mathbb{N}$ , the set of all natural numbers.

= { | is a multiple of 3}

= { | is a multiple of 5}

If all of the natural numbers were to be placed in their appropriate places in the above Venn diagram, which of the following would be placed in the gray region?

$7\textup,916$

CORRECT

$1\textup,565$

$3\textup,890$

$7\textup,431$

$3\textup,966$

Explanation

The gray region is the region outside both and and is therefore the set of natural numbers that are multiples of neither 3 nor 5.

1,565 and 3,890 can be eliminated as choices as each is divisible by 5: the former ends in 5 and the latter ends in 0.

7,431 and 3,966 can be eliminated as each is divisible by 3: $7,431 \div 3 = 2,477$ and $3,966 \div 3 = 1,322$ .

7,916 is not divisible by 5 as it ends in 6; it is not divisible by 3 as $7,916 \div 3 =2,638 ; R; 2$ . Therefore, it is the correct choice.

If two events are independent of one another, there will be no intersection of their circles on a Venn Diagram.

True

CORRECT

False

Explanation

If the two events in a problem are independent, they cannot occur at the same time. That means their circle will not intersect and they will not have a shared middle section.

Venn_4