E. What rule of inference is used in each of the following arguments? Show
solution. (5 pts each)
1. If it will rain today, then the classes are suspended. The classes are not
suspended today. Therefore, it did not rain today.
2. If you read your module today, then you will not play ML today. If you
cannot play ML today, you can play ML tomorrow. Therefore, you read
your module today, then you will play ML tomorrow.
1. Let p represent it will rain today
Let q represent the classes are suspended.
So we have
"p\\to q\\\\\n\\neg q\\\\\n\\therefore \\neg p"
This is Modus Tollens
2. Let p represent You read your module
Let q represent You will play ML today
Let r represent You will play ML tomorrow
"p\\to \\neg q\\\\\n\\neg q \\to r\\\\\n\\therefore p \\to r"
This is Hypothetical Syllogism
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