Question

Let p,q,r denote the statements "It is raining", "It is cold", and "It is pleasant", respectively. Then the statement "It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold" is represented by

• A. $(\rightharpoondown p\wedge r)\wedge (\rightharpoondown r\to (p\wedge q))$
• B. $(\rightharpoondown p\wedge r)\wedge$$((p\wedge q)\to \rightharpoondown r)$
• C. $(\rightharpoondown p\wedge r)\vee$$((p\wedge q)\to \rightharpoondown r)$
• D. $(\rightharpoondown p\wedge r)\vee (r\to (p\wedge q))$

Answer 1

The correct option is A $(\rightharpoondown p\wedge r)\wedge (\rightharpoondown r\to (p\wedge q))$

p: " It is raining", q : "it is cold "' and r : "It is pleasent"
So the correct representation of "It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold" is
$(\rightharpoondown p\vee r)\vee (\rightharpoondown ronlyifp\wedge q)\equiv (\rightharpoondown p\wedge r)\wedge (\rightharpoondown r\to (p\wedge q\left)\right)$