Logic / Unit 4 Logic 130 worked example, 60 to 90 seconds
Symbolizing Compound Statements
The idea
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.
In practice
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.
Where people slip
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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