2) Consider the following two propositions: p: It snows tonight. q: I will stay

2) Consider the following two propositions: p: It snows tonight. q: I will stay home. Use negation (~) conjunction () disjunction () and/or implication () to construct a logical equivalence of pq. Construct the truth table for both statements and explain how the truth tables establish logical equivalences. P Q pq T T T T F F F T T F F T P Q T T T T F F T F F 3) Consider the statement There does not exist a narwhal that can live on land. Write an equivalent English statement that begins with the words Every narwhal Let P(x) be the predicate x can live on land where the variable x represents animals. Write both statements symbolically using P(x) and quantifiers ( ). 5) At a regional competition 7 male runners compete in a 100-meter sprint and 5 female runners compete in a separate 100-meter sprint. How many different arrangements are possible for a first- second- and third-place male runner and a first- and second-place female runner together?