Question

If A = { 2,4,6,8, 10 } , B= { 1,2,3,4,5,6,7,8,9,10 } find

i) (A- B) ∪ (B- A)

ii) (A∪ B) – (A ∩ B).What do you observe.​

Answer 1

SOLUTION :

❒ Given :-

• A = { 2, 4, 6, 8, 10 }

• B = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

❒ To Find :-

• (i) (A – B)∪(B – A)

• (ii) (A∪B) – (A∩B)

❒ Calculation :-

(i)

• ✎ A – B = { 2, 4, 6, 8, 10 } – { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

➜ A – B = { }

• ✎ B – A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } – { 2, 4, 6, 8, 10 }

➜ B – A = { 1, 3, 5, 7, 9 }

• ∴ (A – B)∪(B – A) = { } ∪ { 1, 3, 5, 7, 9 }

⇒ (A – B) ∪ (B – A) = { 1, 3, 5, 7, 9 } ★

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(ii)

• ✎ A∪B = { 2, 4, 6, 8, 10 } ∪ { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

➜ A∪B = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

• ✎ A ∩ B = { 2, 4, 6, 8, 10 } ∩ { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

➜ A ∩ B = { 2, 4, 6, 8, 10 }

• ∴ (A∪B) – (A∩B) = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } – { 2, 4, 6, 8, 10 }

⇒ (A∪B) – (A∩B) = { 1, 3, 5, 7, 9 } ★

____________________________________________

We have got,

If,

• A = { 2, 4, 6, 8, 10 }

• B = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

Then,

• (A – B) ∪ (B – A) = { 1, 3, 5, 7, 9 }

• (A∪B) – (A∩B) = { 1, 3, 5, 7, 9 }

∴ (A – B) ∪ (B – A) = (A∪B) – (A∩B) ★

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KNOW MORE :

If P and Q are any two sets, then

• ➛ P∪Q = x | x ∈ P or x ∈ Q

• ➛ P∩Q = x | x ∈ P and x ∈ Q

• ➛ P – Q = x | x ∈ P, but x ∉ Q

• ➛ (P∪Q)∪(P∩Q) = x | x ∈ (P∪Q) or x ∈ (P∩Q)

• ➛ (P∪Q)∩(P∩Q) = x | x ∈ (P∪Q) and x ∈ (P∩Q)

• ➛ (P∪Q)∪(P – Q) = x | x ∈ (P∪Q) or x ∈ (P – Q)

• ➛ (P∪Q)∩(P – Q) = x | x ∈ (P∪Q) and x ∈ (P – Q)

• ➛ (P∪Q) – (P∩Q) = x | x ∈ (P∪Q), but x ∉ (P∩Q)

• ➛ (P∩Q) – (P∪Q) = x | x ∈ (P∩Q), but x ∉ (P∪Q)