[3 marks sum]

Question 13 Marks

Let n(A) 30, n(B) = 27 and n(A∪B) = 45, find: n(A ∩ B).

Answer

n(A) = 30, n(B) = 27 and n(A ∪ B) = 45
We know that,
n(A ∩ B) = n( A) + n(B) – n( A∪ B)
n(A ∩ B) = 30 + 27 – 45
n(A ∩ B) = 57 – 45 = 12

Question 23 Marks

If A = {even numbers less than 12},
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4} then
State if the following statement is true:
A ⊇ B ⊇ E

Answer

A = {Even number less than 12} = {2, 4, 6, 8, 10}
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4}
A ⊇ B ⊇ E : It is true.

Question 33 Marks

If A = {even numbers less than 12},
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4} then
State if the following statement is true:
E ⊇ B

Answer

A = {Even number less than 12} = {2, 4, 6, 8, 10}
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4}
E ⊇ B : It is false.

Question 43 Marks

If A = {even numbers less than 12},
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4} then
State if the following statement is true:
D ⊄ A

Answer

A = {Even number less than 12} = {2, 4, 6, 8, 10}
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4}
D ⊄ A : It is false

Question 53 Marks

If A = {even numbers less than 12},
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4} then
State if the following statement is true:
D ⊂ C

Answer

A = {Even number less than 12} = {2, 4, 6, 8, 10}
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4}
D ⊂ C : It is false.

Question 63 Marks

If A = {even numbers less than 12},
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4} then
State if the following statement is true
C ⊆ A

Answer

A = {Even number less than 12} = {2, 4, 6, 8, 10}
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4}
C ⊆ A: It is false.

Question 73 Marks

If A = {even numbers less than 12},
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4} then
State if the following statement is true:
B ⊂ A

Answer

A = {Even number less than 12} = {2, 4, 6, 8, 10}
B = {2, 4},
C = {1, 2, 3},
D = {2, 6} and E = {4}
B ⊂ A: It is true

MATHS [3 marks sum]