Symbolizing Compound Statements
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Symbolizing a compound statement means isolating its simple components, assigning a letter to each, choosing the connective the English actually asserts, and placing parentheses so one connective is plainly the main one.
Five sentences. The picnic happens unless it rains: unless names the condition under which the first part fails, giving tilde R horseshoe P. You pass only if you submit: only if marks what follows it as the necessary condition, so the arrow runs from passing to submitting — P horseshoe S. Neither the bridge nor the tunnel is open: both are denied, so tilde B dot tilde T. If the alarm sounds then if the door opens the guard responds: the second conditional sits inside the first — A horseshoe, open bracket, D horseshoe G, close bracket. Last: he studies and he passes or he retakes it. Without brackets that has two readings, so the intended one must be marked — S dot, open bracket, P wedge R, close bracket. Name the main connective each time as the check.
Only if and if are opposite instructions and one word apart. If S then P puts the arrow from S to P; P only if S puts it from P to S. Symbolizing one as the other reverses the conditional, and every truth table built on it is then correct work on the wrong statement.
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