Math 9th Chap 3 : Topic 3 - Maryam Publications

Math Chapter 3 : Topic 3

Venn Classification

1 / 25

Which law states that $A \cup B = B \cup A$?

A) Identity law

B) Commutative law

C) Distributive law

D) Associative law

2 / 25

Which law is represented by $(A \cap B) \cap C = A \cap (B \cap C)$?

A) Distributive law

B) Associative law

C) Commutative law

D) Identity law

3 / 25

The correct identity law for union is:

A) $A \cap U = \varnothing$

B) $A \cap \varnothing = A$

C) $A \cup \varnothing = A$

D) $A \cup \varnothing = \varnothing$

4 / 25

Which of the following is true?

A) $A \cap U = \varnothing$

B) $A \cup U = A$

C) $A \cap U = A$

D) $A \cup \varnothing = U$

5 / 25

Which law is used in $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$?

A) Commutative law

B) Identity law

C) Associative law

D) Distributive law

6 / 25

In a Venn diagram, $A \cap B \cap C$ represents:

A) Elements in $A$ only

B) Elements in $B$ only

C) Elements outside all sets

D) Common elements of all three sets

7 / 25

Which property is always true?

A) $A \cap A = A$

B) $A \cup A = \varnothing$

C) $A \cup A = U$

D) $A \cap A = \varnothing$

8 / 25

The commutative law for intersection is:

A) $A \cap B = U$

B) $A \cap B = B \cap A$

C) $A \cap B = A \cup B$

D) $A \cap B = \varnothing$

9 / 25

Which expression shows distributive property correctly?

A) $A \cup B \cup C$

B) $A \cap (B \cup C)$

C) $A \cap B \cap C$

D) $A \cup (B \cap C)$

10 / 25

$A \cap (B \cup C)$ equals:

A) $A \cap B \cap C$ only

B) $(A \cap B) \cup (A \cap C)$

C) $A \cup (B \cap C)$

D) $(A \cup B) \cap C$

11 / 25

Which law helps in simplifying Venn diagram regions?

A) De Morgan's law only

B) Geometry law

C) Arithmetic law

D) Set laws (union & intersection properties)

12 / 25

If $A \cup \varnothing = A$, then $\varnothing$ is called:

A) Complement set

B) Identity element of union

C) Universal set

D) Null set of intersection

13 / 25

Which of the following is true for intersection?

A) $A \cap U = A \cup U$

B) $A \cap U = A$

C) $A \cap U = U$

D) $A \cap U = \varnothing$

14 / 25

Which region is shaded in $A \cup B \cup C$?

A) Only overlapping region

B) Only $A$ region

C) Outside circles

D) All three circles

15 / 25

Which of the following is $NOT$ a law of sets?

A) Commutative law

B) Associative law

C) Distributive law

D) Gravitational law

16 / 25

If $A \cap B = B \cap A\ $, this proves:

A) Null law

B) Identity law

C) Commutative law

D) Associative law

17 / 25

Which is correct?

A) $A \cap (A \cup B) = \varnothing$

B) $A \cup B = \varnothing$ always

C) $A \cap B = U$ always

D) $A \cup (A \cap B) = A$

18 / 25

In Venn diagrams, union is represented by:

A) Empty region

B) Outside region

C) All shaded areas of sets involved

D) Only overlapping part

19 / 25

Which is true for three sets $A$, $B$, $C$?

A) $A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$

B) $(A \cap B) \cup C = A \cap (B \cup C)$

C) $(A \cup B) \cap C = A \cup (B \cap C)$

D) $A \cup B = A \cap B$ always

20 / 25

Which law explains grouping change in $A \cup (B \cup C)$?

A) Associative law

B) Identity law

C) Absorption law

D) Commutative law

21 / 25

If $A \cup U = U$, then $U$ is called:

A) Neutral element

B) Empty set

C) Dominating element

D) Identity element of union

22 / 25

Which of the following is correct for any set $A$?

A) $A \cup \varnothing = \varnothing$

B) $A \cap \varnothing = A$

C) $A \cup \varnothing = A$

D) $A \cap U = \varnothing$

23 / 25

Which region is $NOT$ included in $A \cap B \cap C$?

A) Only $B$ region

B) Outside all sets

C) Only $A$ region

D) Common part of all three

24 / 25

Which property is shown in $A \cap (A \cup B) = A$?

A) Identity law

B) Commutative law

C) Absorption law

D) Distributive law

25 / 25

In Venn diagrams, laws of sets are useful because they:

A) Replace numbers

B) Eliminate sets

C) Remove need for diagrams

D) Simplify overlapping regions logically

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