Let 𝑝 and 𝑞 be the proposition variables denoting𝑝: It is below freezing.𝑞: It is snowing.Write the following propositions using variables, 𝑝 and 𝑞, and logical connectives.a. It is below freezing and snowingb. It is below freezing but not snowingc. It is not below freezing and it is not snowing.d. It is either snowing or below freezing (or both).e. If it is below freezing, it is also snowing.f. It is either below freezing or it is snowing, but it is not snowing if itis below freezing.g. That it is below freezing is necessary and sufficient for it to besnowing

Required informationSkip to questionNOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.Let p and q be the propositionsp: It is below freezing.q: It is snowing.The compound proposition for the statement "It is either snowing or below freezing (or both)" is p ∧ q.Group startsTrue or FalseTrue, unselectedFalse, unselected

Consider the statement given below and state its dual.Weather is cloudy and it is raining.Question 1Answera.It is not raining, and weather is not cloudy.b.Weather is cloudy, or it is not raining.c.Weather is not cloudy, and it is raining.d.It is raining, or weather is cloudy.

Which of the following statements is logically equivalent to the statement "If it is raining, then the ground is wet"?A. If the ground is wet, then it is raining.B. If it is not raining, then the ground is not wet.C. If the ground is not wet, then it is not raining.D. All of the above

Suppose the domain of the propositional function 𝑃(𝑥, 𝑦) consists of pairs 𝑥 and 𝑦, where 𝑥 is 2, or 5and 𝑦 is 1, 2, or 3. Write out these propositions using disjunctions and conjunctions.a) ∀𝑥∀𝑦𝑃 (𝑥, 𝑦) b) ∃𝑥∃𝑦𝑃 (𝑥, 𝑦) c) ∃𝑥∀𝑦𝑃 (𝑥, 𝑦) d) ∀𝑦∃𝑥𝑃 (𝑥, 𝑦)

. What is the conjunction of the statements "It is sunny" and "It is warm"?*2 pointsA) It is sunny and warm.B) It is sunny or warm.C) It is neither sunny nor warm.D) It is sunny but not warm.