Question

s is a subset within a universal set, u. if s = {x, y, 4, 9,?}, which could describe u? u = {keys on a keyboard} u = {letters} u = {numbers} u = {punctuation marks}

Explanation:

To determine the universal set \( U \) that can contain the subset \( S = \{x, y, 4, 9,?\} \), we analyze each option:

• Option 1: \( U = \{\text{keys on a keyboard}\} \). A keyboard has letters (like \( x, y \)), numbers (like \( 4, 9 \)), and punctuation marks (like \(? \)), so \( S \) can be a subset of this set.
• Option 2: \( U = \{\text{letters}\} \). The set \( S \) contains numbers (\( 4, 9 \)) and a punctuation mark (\(? \)), which are not letters, so \( S \) cannot be a subset of this set.
• Option 3: \( U = \{\text{numbers}\} \). The set \( S \) contains letters (\( x, y \)) and a punctuation mark (\(? \)), which are not numbers, so \( S \) cannot be a subset of this set.
• Option 4: \( U = \{\text{punctuation marks}\} \). The set \( S \) contains letters (\( x, y \)) and numbers (\( 4, 9 \)), which are not punctuation marks, so \( S \) cannot be a subset of this set.

Answer:

A. \( U = \{\text{keys on a keyboard}\} \)