Use counting to determine the whole number that corresponds to the cardinality of these sets. (a) $$ A=\{x \mid x \in N $$ and $$ 16

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Let's first analyze set A.

(a) A = { x ∈ N | 16 < x ≤ 26 }

Since "N" represents the set of natural numbers, and the condition 16 < x ≤ 26 means x can be any natural number greater than 16 up to and including 26. Listing them out:

x = 17, 18, 19, 20, 21, 22, 23, 24, 25, 26

There are 10 numbers, so n(A) = 10.

Now, consider set B.

(b) B = { x ∈ N | x – 5 = x }

Solve the equation x – 5 = x:
 Subtract x from both sides:
  x – 5 – x = 0  ⟹  -5 = 0
This is a contradiction, meaning no natural number x satisfies the equation. Thus, B is the empty set.

The cardinality of B is 0.

Final answers: 
(a) n(A) = 10  
(b) n(B) = 0
(a) n(A) = 10 (b) n(B) = 0

Use counting to determine the whole number that corresponds to the cardinality of these sets. (a) \( A=\{x \mid x \in N \) and \( 16

Ask by Guzman Young. in the United States

Feb 27,2025

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Use counting to determine the whole number that corresponds to the cardinality of these sets. (a) \( A=\{x \mid x \in N \) and \( 16 Ask by Guzman Young. in the United States Feb 27,2025