Verify Set Properties and Identities

In this lesson, you will be given various sets and an expression. You have to resolve their left and right side and conclude whether the given expression is a valid and verified property or not.

Question 1:

Test the expression:

$A \cup B$ $=$ $B \cup A$

For the sets:

A=\{ 3 , z , 1 , f \}

B=\{ f , x , 2 \}

Fill both sides and check equality.

A \cup B

=

B \cup A

The expression is: EqualUnequal

Question 2:

Test the expression:

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

For the sets:

A=\{ 9 , j , 7 , d , 8 \}

B=\{ 7 , j , z , h , 8 \}

Fill both sides and check equality.

A \cap B

=

B \cap A

The expression is: EqualUnequal

Question 3:

Test the expression:

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

For the sets:

A=\{ j , r , 7 , 8 \}

B=\{ j , 7 \}

C=\{ 5 , z , 1 \}

Fill both sides and check equality.

(A \cup B) \cup C

=

A \cup (B \cup C)

The expression is: EqualUnequal

Question 4:

Test the expression:

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

For the sets:

A=\{ u , w , j , k , z \}

B=\{ w , k , j , 4 \}

C=\{ k , w , u , 3 \}

Fill both sides and check equality.

(A \cap B) \cap C

=

A \cap (B \cap C)

The expression is: EqualUnequal

Question 5:

Test the expression:

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

For the sets:

A=\{ h , t \}

B=\{ w , q , r \}

C=\{ r , h \}

Fill both sides and check equality.

A \cup (B \cap C)

=

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

The expression is: EqualUnequal

Question 6:

Test the expression:

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

For the sets:

A=\{ f , 4 \}

B=\{ j , t \}

C=\{ b , j , s , f , q \}

Fill both sides and check equality.

A \cap (B \cup C)

=

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

The expression is: EqualUnequal

Question 7:

Test the expression:

$(A \cup B)^c$ $=$ $A^c \cap B^c$

For the sets:

U=\{ i , s , 8 , o , 0 , 9 , 7 \}

A=\{ i , s , 8 , 0 \}

B=\{ i , 0 , 9 \}

Fill both sides and check equality.

(A \cup B)^c

=

A^c \cap B^c

The expression is: EqualUnequal

Question 8:

Test the expression:

$(A \cap B)^c$ $=$ $A^c \cup B^c$

For the sets:

U=\{ i , s , q , e , g , d , p \}

A=\{ e , q \}

B=\{ e , d , q , s , g \}

Fill both sides and check equality.

(A \cap B)^c

=

A^c \cup B^c

The expression is: EqualUnequal

End of Lesson