Q1. [1 point] Which of these sentences are propositions? a) x * 2 = 14. b) Moham

Question

Q1. [1 point] Which of these sentences are propositions? a) x * 2 = 14. b) Mohamed will pass the exam c) 15-7-10. d) Answer this question. Q2. [2 points] What is the negation of each of these propositions? a) Fatima has an MP3 player and an iPhone b) There is no pollution in New Jersey. c) 2+1-3 d) The winter in Cairo is neither hot nor sunny. Q3. [3 points] Let p and q be the propositions p: It is below freezing. q: It is snowing. Write these propositions using p and q and logical operators: a) b) c) d) e) f) It is below freezing and snowing. It is below freezing but not snowing. It is not below freezing and it is not snowing. It is neither snowing nor below freezing. Either it is below freezing or it is snowing, but it is not snowing if it is below freezing. That it is below freezing is necessary and sufficient for it to be snowing.

Explanation / Answer

As per Chegg policy, I am answering only first 4 subparts.

Q1.) Propositions are assertion for which you can assign the logical value either true or false.

a.) Since result of above inequality depends on the value of x. That is for value of x, result will change. Therefore, it is not proposition.

b.) It is a propostion as we can assign a logical value to it.

c.) It is also a proposition as it gives a certain value i.e., false in this case.

d.) It is not a proposition as it doesn't give any logical value

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