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here were given two simple statements P and Q P is the statement theres life on Mars Q is the statement theres life on Europa we want to write each of these given statements in symbolic form for the first one the statement says there is life on both Mars and Europa so thats equivalent to saying theres life on Mars and theres life on Europa therefore that looks like the symbol P and Q both of them connected with the and operator so we would write that symbolically as P and then remember the and symbol is this upward pointing wedge P and Q for Part B there is life on neither Mars nor Europa in simple form thats the same as saying there is not life on Mars and there is not life on Europa thats what the neither/nor means so its not P and not Q and we write that this way not P and not Q and thats the symbolic form for that statement Part C says there is life on Mars so that would be P but not on Europa in these logical statements the word but often means the same thing as the word