Back to Exercise: Venn Diagrams with Two Events

Exercises: Venn Diagrams with Two Events

Work through each section in order. For the diagram problems, place elements in the intersection first, then the parts that belong to only one set, and last the region outside both circles. Always check that every element sits in exactly one region.

Grade 7·18 problems·~30 min·Uganda NCDC Primary 7 Mathematics·lesson·sets-03

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Recall / Warm-Up

These problems review set membership and subsets from earlier lessons.

$An oval labelled A containing the numbers 2, 4, 6, 8, with 5 and 7 shown outside it$

The set $A = \{2, 4, 6, 8\}$ . Which statement is true?

$6 \in A$ and $5 \notin A$

$5 \in A$ and $6 \notin A$

$7 \in A$ and $4 \notin A$

$2 \notin A$ and $8 \notin A$

$A two-circle Venn diagram inside a rectangle, with the four regions marked P, Q, R, S and the rectangle corner marked with a question mark$

In a two-circle Venn diagram, the rectangle that surrounds both circles stands for which set?

The empty set

The universal set $E$

The intersection $A \cap B$

The union $A \cup B$

A group of learners is listed as $\{Ana, Ben, Cora, Deo, Efua\}$ . How many learners are in the group?

Fluency Practice

$A blank two-circle Venn diagram with universal set E, set A football, set B volleyball, and four regions numbered 1 to 4$

On a two-circle Venn diagram, which region holds learners who like football but not volleyball?

Region 1, the A-only crescent

Region 2, the centre overlap

Region 3, the B-only crescent

Region 4, outside both circles

$A two-circle Venn diagram with the number 6 written twice, once in the A-only crescent and once in the overlap, each marked with a question mark$

The number 6 has been written in the A-only crescent AND again in the overlap. In which single region does 6 belong, given that 6 is in both $A$ and $B$ ?

In the A-only crescent

In the overlap $A \cap B$ only

In both the crescent and the overlap

In the region outside both circles

$A blank two-circle Venn diagram with universal set E and empty circles A and B, ready for elements to be placed$

For $E = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$ , $A = \{$ multiples of 3 $\}$ , $B = \{$ multiples of 4 $\}$ . How many elements go in the overlap $A \cap B$ ?

$A completed two-circle Venn diagram: A only holds 2, 4, 8; the overlap holds 6; B only holds 3, 9; and 1, 5, 7 lie outside both circles$

Using the completed diagram, find $n(A \cup B)$ .

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