1. Let p, q, and r be the following propositions: p = "it is raining." q = "the sun is shining." r = "there are clouds in the sky." Translate the following into logical notation, using p, q. r, and logical connectives. (a) It is raining and the sun is shining. (b) If it is raining, then there are clouds in the sky. (c) If it is not raining, then the sun is not shining and there are clouds in the sky. (d) The sun is shining if and only if it is not raining.

Q: 2) Write the converse, inverse, and contrapositive of the proposition. If |x> 2 then x > 2 or x<-2

A:

Q: (a) Suppose P, Q and R are statements. Complete the following truth table for the statement "(PQ)…

A: First, let's recall what the implications mean:P⇒Q is true except when P is true and Q is false.Q⇒¬R…

Q: 17. Let p, q and r be the propositions p: Grizzly bears have been seen in the area. q: Hiking is…

A: 17)Proposition (a): Statement: Berries are ripe along the trail, but grizzly bears have not been…

Q: 4. Use Green's Theorem of the Plane to evaluate the following closed path integral. xy2 dx+ 2x2y dy…

A: According to green’s theorem closed path integral over the curve C is calculated by,

Q: Define the following propositions: a : It is a raining day. b: Jack comes to the party. c: Jack is…

A: See the detailed solution below.

Q: Let p, q, and r be the propositions p: It is hot. q: It is raining. r: We go to the beach. Match the…

A:

Q: Let p, q, and r be the following propositions: p: The user enters a valid password q: The account is…

A:

Q: Reduce the proposition using laws, including de Morgan's and conditional. Simplify (q∨n)∧¬(¬q∧n) to…

A: (q∨n)∧¬(¬q∧n)apply the complement and use De Morgan's Law(q∨n)∧(¬¬q∨¬n) simplify