which diagram represents the following sets? p = {x | x is an integer divisible by 2}; q = {x | x is an odd…
which diagram represents the following sets? p = {x | x is an integer divisible by 2}; q = {x | x is an odd integer}; r = {x | x is an integer divisible by 3}
Answer
Explanation:
Step1: Analyze set - element properties
Set (P) contains even integers (divisible by 2), set (Q) contains odd integers. So (P\cap Q=\varnothing) (empty - set), since an integer cannot be both even and odd.
Step2: Analyze intersections with set (R)
Set (R) contains integers divisible by 3. Some even integers are divisible by 3 (e.g., 6), so (P\cap R\neq\varnothing). Some odd integers are divisible by 3 (e.g., 3, 9), so (Q\cap R\neq\varnothing).
Answer:
The first diagram (where (P) and (Q) are non - overlapping, and both (P) and (Q) overlap with (R)) represents the sets.