the diagram represents three statements about animals at the zoo: p, q, and r. for how many animals is (p ∨…
the diagram represents three statements about animals at the zoo: p, q, and r. for how many animals is (p ∨ q) ∧ r true? 15 17 20 22
Answer
Answer:
15
Explanation:
Step1: Recall logical - OR and AND rules
The expression ((p\vee q)\wedge r) means that either (p) or (q) is true and (r) is true.
Step2: Identify relevant regions in Venn - diagram
The regions for (p\vee q) are all parts of (p) and (q) combined. The regions for (r) is the circle labeled (r). The intersection ((p\vee q)\wedge r) consists of the parts of (r) that overlap with either (p) or (q).
Step3: Calculate the number
The overlapping regions of (r) with (p) or (q) are the regions with values (9), (2), and (4). So, (9 + 2+4=15).