q ∧ ∼r
∧ symbol indicates conjunction and it is read as "and".
∼ symbol is read as negation.
∼r means "not r"
Hence, q ∧ ∼r means q and not r.
q and not r is the elements that are in q but not in r.
Hence, the venn diagram given by option C indicates q ∧ ∼r .
(p∨r)∧q
∨ symbol indicates disjunction and it is read as "or".
Hence, p∨r is read as p or r.
p or r means the elements that are either in p or r.
(p∨r)∧q means (p∨r) and q. It indicates the set of elements that are common to (p∨r) and q.
The venn diagram given by option A indicates (p∨r)∧q.
(q∧r)∨(∼p∧r).
q∧r means q and r. It indicates elements that are common to both q and r
∼p∧r means not p and r. It indicates elements in r but not in p.
(q∧r)∨(∼p∧r) means (q∧r) or (∼p∧r). It indicate elements that are either in q∧r or ∼p∧r.
Hence, the venn diagram given by option B indicates (q∧r) ∨ (∼p∧r).