Please answer questing 24 Q24 If θ = { x : x ∈N and x ≤10} - Maths - Sets

Question

Please answer questing 24

Q24 If θ = { x : x  ∈ N and x ≤ 10}
A = { x : x is prime and x ≤ 10}
B = { x : x is a factor of 24}

Verify the following result

(i) A – B = A âŒ’ B'

(ii) (A ∪ B)' = A' âŒ’ B'

(iii) (A âŒ’B)' = A' ∪ B'

Aarushi Mishra · Accepted Answer

θ=x:x∈ℕ and x≤10θ=1, 2, 3,
, 10Assuming θ to be universal setA=x:x is prime and x≤10A=2, 3, 5, 7B=x:x is a fator of 24 24=3×824=3×2×424=6×424=12×224=24×1B=1, 2, 3, 4, 6, 81
A-B=5, 7B'=5,7,9,10A∩B'=5,7Therefore, A-B=A∩B'2
A∪B=1, 2, 3, 4, 5, 6, 7, 8A∪B'=9, 10A'=1, 4, 6, 8, 9, 10B'=5,7,9,10A'∩B'=9,10HenceA∪B'=A'∩B'3
A∩B=2, 3A∩B'=1, 4, 5, 6, 7, 8, 9, 10A'=1, 4, 6, 8, 9, 10B'=5,7,9,10A'∪B'=1, 4, 5, 6, 7, 8, 9, 10HenceA∩B'=A'∪B'

Please answer questing 24 Q24. If θ = { x : x ∈ N and x ≤ 10} A = { x : x is prime and x ≤ 10} B = { x : x is a factor of 24} Verify the following result (i) A – B = A ⌒ B' (ii) (A ∪ B)' = A' ⌒ B' (iii) (A ⌒B)' = A' ∪ B'

Please answer questing 24

Q24. If $θ$ = { x : x _$\in$N and x $\leq$ 10}
A = { x : x is prime and x $\leq$ 10}
B = { x : x is a factor of 24}

Verify the following result

(i) A – B = A ⌒ B'

(ii) (A $\cup$ B)' = A' ⌒ B'

(iii) (A ⌒B)' = A' $\cup$ B'