Question

In each of the following, find A ∪ B and A ∩ B : i) A= { x: x is an integer divisible by 3 } B= { x: x is a positive integer} ii) A= { x: x ε N and 1 < x ≤ 6} B= { x: x ε N and 6 < x ≤ 10}

Answer 1

Answer:

(i)A= {6,9,12,........}

B= {1,2,3,4,5,6,7,8,9,10,11,12......}

(ii)A= {1,2,3,4,5}

B= {6,7,8,9}

Step-by-step explanation:

A U B = {1,2,3,4,5,6,7,8,9,12}

A n B = {1,2,3,4,5,6,7,8,9,10,11,12}

Answer 2

The correct answers are i) A U B = {..., -9, -6, -3 ,0, 1, 2, 3,...} and A ∩ B = {3, 6, 9,...} and ii) A U B = {2, 3, 4, 5, 6, 7, 8, 9, 10} and A ∩ B = { }.

• i) A= { x: x is an integer divisible by 3 }

• B= { x: x is a positive integer}
• A is the set of all the integers that are divisible by 3.
• Integers that are divisible by 3 include negative and positive multiples of 3.
• ⇒ A = {..., -9, -6, -3 ,0, 3, 6, 9,...}
• B is the set of all the positive integers.
• ⇒ B = {1, 2, 3,...}
• The union of sets gives us a set with elements that are common to
• every set.
• A ∪ B is the collection of all the elements of sets A and B.
• ∴ A U B = {..., -9, -6, -3 ,0, 1, 2, 3,...}
• The intersection of sets gives us elements common to each set.
• A ∩ B is the collection of elements that are common to sets A and B.
• We observe that the elements common to A and B are the positive multiples of 3.
• ∴ A ∩ B = {3, 6, 9,...}
• Hence, A U B = {..., -9, -6, -3 ,0, 1, 2, 3,...} and A ∩ B = {3, 6, 9,...}.

• ii) A = { x: x ∈ N and 1 < x ≤ 6}

• B = { x: x ∈ N and 6 < x ≤ 10}
• A is the set of natural numbers greater than 1 and less than or
• equal to 6.
• ⇒ A = {2, 3, 4, 5, 6}
• B is the set of natural numbers greater than 6 and less than or
• equal to 10.

        ⇒ B = {7, 8, 9, 10}

        The union of sets gives us a set with elements that are common to

        every set.

• A ∪ B is the collection of all the elements of sets A and B.

       ∴ A U B = {2, 3, 4, 5, 6, 7, 8, 9, 10}

        The intersection of sets gives us elements common to each set.

• A ∩ B is the collection of elements that are common to A and B.
• We observe that no elements are common to sets A and B.
• ∴ A ∩ B = { }, a null set.
• Hence, A U B = {2, 3, 4, 5, 6, 7, 8, 9, 10} and A ∩ B = { }.

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