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

Question

UpStudy AI · Accepted Answer

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

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Pre Algebra Questions

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