25) In a group of 400 readers who read science fiction or literacy works or both, 250 read...
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- In a group of 400 readers who read science fiction or literacy works or both, 250 read science
fiction and 230 read literacy works. How many read both science fiction and literacy works?
Show answer & explanation
This is a set theory problem based on the Principle of Inclusion-Exclusion. The number of people who read both is the sum of the individual groups minus the total number of unique readers.
Step-by-step Derivation:
Step 1: Identify the given values. Total readers (N(S ∪ L)) = 400. Readers of science fiction (N(S)) = 250. Readers of literacy works (N(L)) = 230.
Step 2: Apply the Principle of Inclusion-Exclusion formula: N(S ∪ L) = N(S) + N(L) - N(S ∩ L).
Step 3: Substitute the values into the formula: 400 = 250 + 230 - N(S ∩ L).
Step 4: Simplify the equation: 400 = 480 - N(S ∩ L).
Step 5: Solve for N(S ∩ L): N(S ∩ L) = 480 - 400 = 80.
Step 6: The number of readers who read both is 80.