Analyze the logical form of the following statements using only the connectives $,^,$ and $\_.($a$)$ Either Alice, Bob, and Jones are in the room, but the three of them are not all in the room at the same time. $($b$)$ Either Alice is wearing sun glasses or wearing a hat or wearing both. $($c$)$ It is not the case that today is not Friday. $2.$ Which of the following are well$-$formed formulas? $($a$)\%.($b$)\%$&$($& $^\%).($c$),.($d$)(\%\_$&$)($& $^\text{'}).3.($a$)$ Is the following argument valid? Explain why or not. You can use your intuitions here. Today is Friday. Therefore, tomorrow is Saturday. $($b$)$ Represent the following argument using propositional logic: Today is Friday. Therefore, tomorrow is Saturday. Is the argument valid in propositional logic? That is$,$ represent the proposition Today is Friday. and the proposition Tomorrow is Saturday. using symbols like $\%,$&$,...$ and logical connectives $,\_,^,$ and then check if the argument is valid using a truth table. $4.$ Make a truth table for the following well$-$formed formulas.