If A = { x : x text{ is a natural number} },B | vedclass

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(A) Given sets are:$A = \{1, 2, 3, 4, 5, \ldots \}$$B = \{2, 4, 6, 8, \ldots \}$$C = \{1, 3, 5, 7, 9, \ldots \}$$D = \{2, 3, 5, 7, 11, \ldots \}$The i

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$C \cap D = \{ x : x 	ext{ is an odd prime number} \}$

Vedclass · Answer

(A) Given sets are:$A = \{1, 2, 3, 4, 5, \ldots \}$$B = \{2, 4, 6, 8, \ldots \}$$C = \{1, 3, 5, 7, 9, \ldots \}$$D = \{2, 3, 5, 7, 11, \ldots \}$The intersection $C \cap D$ consists of elements that are common to both set $C$ (odd natural numbers) and set $D$ (prime numbers).Since $2$ is the only even prime number,all other prime numbers are odd.Therefore,$C \cap D = \{ x : x 	ext{ is an odd prime number} \} = \{3, 5, 7, 11, \ldots \}$.

If $A = \{ x : x \text{ is a natural number} \}$,$B = \{ x : x \text{ is an even natural number} \}$,$C = \{ x : x \text{ is an odd natural number} \}$,and $D = \{ x : x \text{ is a prime number} \}$,find $C \cap D$.

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