1. Translate the proposition to symbolic form (including delimiters) using the indicated variable:     " If we reduce greenhouse gas emissions (P), then we have a chance to save the planet (Q), but if we don't, then we will regret it (S)."

Write the correct symbolic form (including delimiters) of the following compound propositions using the indicated variable. (6 points)Both Smith (S) and Jones (J) are wearing bow-ties and one of them is wearing a hat (W, H).Man-made climate change will get worse (L) and natural disasters will become more frequent (N) if we don't make radical changes (Z).

2. Translate the proposition to symbolic form (including delimiters) using the indicated variable:     "Paula (P) and Quentin (Q) are going to the pub but Roger (R) won't go if Sandra (S) does."

Select the option that best completes the following sentence. The effect of greenhouse gases in Earth's atmosphere is to:absorb ultra-violet and other high-energy radiation from the Sun, protecting the Earth's surfacereflect sunlight back into spaceretain some of the heat emitted from the Earth's surfacetrap heat in the lower atmosphere so that none can escape into space

pp ∧q→ r ∧sq¬s------ris a valid argument.

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