Help quick please

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Okay, so I'm assuming you need help understanding this example?This goes like this:You have a proposition:= 'Pizza is great'. This proposition has 2 predicates, P(x) which says 'x' is pizza, and G(x) which says 'x' is great. This basically says 'x' is pizza and 'x' is great (pizza is great). Then we have the statement in logical notation. P(x)--->G(x), this says that if P(x) is true then G(x) is true. Subsequently, this statement will only be true if G(x) is true because G(x) is the conclusion. For a statement to be true its conclusion also has to be true otherwise if the conclusion of a statement is false, the entire statement will be false. For the second example, I think you have mistakenly written the wrong notation if you are referring to 'some red AND green marbles where R(x) is red marbles and G(x) is green marbles then its logical notation will be:(R(x) ∧ G(x))This represents that there are both; some red and some green marbles. This statement will be false if either of the marbles is missing.I hope that clarify, do let me know if you need any further information.

Answer

a.)P(X):X is a pizzaQ(x):X is great∀x((P(x)->Q(x))b.)R(x):X is a red marbleQ(x):X is a green marble∃x(R(x)∧Q(x))

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