Sets, Relations & Functions
Venn Diagrams and Set Operations
Grade 11
<p>A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% of the people read both the newspapers, then a possible value of x can be</p>
Step-by-Step Solution
Key Concept: Use the principle that the union of two sets cannot exceed the total population, and the intersection cannot exceed either individual set.
<p><strong>Step 1:</strong> Given, $n(A) = 63$, $n(B) = 76$ and $n(A \cap B) = x$</p><p><strong>Step 2:</strong> We know that, $n(A \cup B) = n(A) + n(B) - n(A \cap B)$</p><p><strong>Step 3:</strong> Since $n(A \cup B) \leq 100$, we have:</p><p>$$100 \geq 63 + 76 - x$$</p><p>$$x \geq 139 - 100$$</p><p>$$x \geq 39$$</p><p><strong>Step 4:</strong> Also, $n(A \cap B) \leq n(A)$, so:</p><p>$$x \leq 63$$</p><p><strong>Step 5:</strong> Therefore, $39 \leq x \leq 63$</p><p>∴ Answer is (a) 55, which lies in this range.</p>
Correct Answer: A