Logic Puzzle 1 Whom to invite for the party: If you invite John, - - PowerPoint PPT Presentation

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Sep 07, 2022 294 likes •420 views

Logic Puzzle 1 Whom to invite for the party: If you invite John, you must invite Paul. You must invite either Paul or Mary, but not both. You must invite either John or Mary or both. If you invite Mary, you must also invite John.

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Logic Puzzle 1

Whom to invite for the party:

◮ If you invite John, you must invite Paul. ◮ You must invite either Paul or Mary, but not both. ◮ You must invite either John or Mary or both. ◮ If you invite Mary, you must also invite John.

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Solution with Truth Table

invite John invite Paul invite Mary false false false true false false false true false false false true true true false true false true false true true true true true

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If you invite John, you must invite Paul.

invite John invite Paul invite Mary false false false true false false false true false false false true true true false true false true false true true true true true

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You must invite either Paul or Mary, but not both.

invite John invite Paul invite Mary false false false true false false false true false false false true true true false true false true false true true true true true

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You must invite either John or Mary or both.

invite John invite Paul invite Mary false false false true false false false true false false false true true true false true false true false true true true true true

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If you invite Mary, you must also invite John.

invite John invite Paul invite Mary false false false true false false false true false false false true true true false true false true false true true true true true The only possible solution is to invite John and Paul, but not Mary.

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Logic Puzzle 2

Here’s another party:

◮ You should not (not invite Charlie or not invite Susan). ◮ If you don’t invite Diana, Mary will not come either. ◮ If you invite Susan, you should not invite (Paul or John). ◮ You should not invite Charlie or not invite Diana.

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Logic Puzzle 2: Solution

In this case a truth table would have to be quite large because so many people are involved. It is probably easier to apply De Morgan’s law:

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De Morgan’s Law:

You should not (not invite Charlie or not invite Susan). Is the same as You should invite Charlie and invite Susan.

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De Morgan’s Law:

You should not invite Charlie or not invite Diana. Is the same as You should not invite (Charlie and Diana).

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Therefore:

◮ You should invite Charlie and invite Susan. ◮ If you don’t invite Diana, Mary will not come either. ◮ If you invite Susan, you should not invite (Paul or John). ◮ You should not invite (Charlie and Diana).

The first, fourth and second lines imply that implies Charlie must come; Diana cannot come; Mary cannot come. The first and third lines imply that you should invite Susan, but not Paul and not John.

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