Q20-5 points Prove that for any sets A and B, (A ∪ B) ∩ B  =  B.

Q1-6 points Let ​p​ = “The sky is blue.” Let ​q​ = “The sky is cloudy.” Convert into symbols:   “If the sky is blue, then the sky is not cloudy.”

Q2-6 points Determine the truth value of the statement:                          (−9 < −3)  ∨ (5²​  = 49)   Write True or False for the answer.

Q4-6 points Create a truth table for the statement:                                                                                                                                                                                                            r  ⇒ (​p ​∨ ​q​)  

Q9-8 points Consider the propositional values:   p​(​n​): ​n​ is prime q​(​n​): ​n​ is even r​(​n​): ​n​ > 2                                                       Express the following in words: ∀n ∈ Z [(q(n) ⋀ r(n)) ⇒ ~ p(n)] 

The nurse is caring for an infant with myelomeningocele who is scheduled for surgical repair in the morning. Which of the following is not considered as an early sign of infection should the nurse monitor on this infant? 

Q13-6 points Prove by induction:   2 + 8 + 14 + … + (6n − 4) = ​n​(​3n​ ​​− 1)

Q1-6 points Let ​p​ = “It is extremely humid.” Let ​q​ = “It will rain tomorrow.” Convert into symbols:   “If it is extremely humid, then it will rain tomorrow.”

Q10-6 points Prove the statements are equivalent using a truth table:             ~ (​p ​∨ ​q​) ​≡​ (​~ ​p ​∧ ~ ​q​)

Q14-6 points Prove the statement (if true), or disprove it by giving a counterexample (if false)    Assume that x and y are real numbers. If x² = y², then x = y.