GEK1505-tut01 - National University of Singapore Department...

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National University of Singapore Department of Mathematics GEK1505 Living with Mathematics Tutorial 1 1. A Cretan said, “All Cretans are liars.” Assuming that no self-contradictory statements are made, can he be telling the truth? Can he be the only Cretan in existence? Does there exist any Cretan who tells the truth? 2. Express the following statements in terms of “simple” statements con- nected by “and”, “or”, “not”. (a) Although he loves food, he eats neither chicken nor beef. (b) Either both Jack and Jill are innocent, or else only Jack is guilty. (c) At most two of the persons Tom, Dick and Harry committed the robbery. 3. Express the following statements as “implications”. Write down their negations, converses, inverses and contrapositives. (a) Where there is a will, there is a way. (b) No venture, no gain. (c) There is no smoke without fire. (d) Easy come, easy go. 4. It is agreed that if everybody brings food into the cinema, the cinema
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This note was uploaded on 09/16/2011 for the course SCIENCE GEK1505 taught by Professor Leong during the Spring '11 term at National University of Singapore.

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GEK1505-tut01 - National University of Singapore Department...

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