The Logic Book 6th Edition: Ch 3.5, q. 4: Symbolize the following arguments and

Question

The Logic Book 6th Edition: Ch 3.5, q. 4:

Symbolize the following arguments and use truth-tables to test for truth-functional validity. Use full truth-tables to establish truth-functional validity and shortened truth-tables to establish truth-functional invalidity.

f) If the butler murdered Devon, then the maid is lying, and if the gardener murdered Devon, then the weapon was a slingshot. The maid is lying if and only if the weapon wasn't a slingshot, and if the weapon wasn't a slingshot, then the butler murdered Devon. Therefore the butler murdered Devon.

Explanation / Answer

If the butler murdered Devon, then the maid is lying,

and if the gardener murdered Devon, then the weapon was a slingshot. The maid is lying if and only if the weapon wasn't a slingshot, and if the weapon wasn't a slingshot, then the butler murdered Devon. Therefore the butler murdered Devon.

The maid is lying if and only if the weapon wasn't a slingshot:Q is TRUE and s is False

then p only True r must false.

   i.e the butler murdered Devon.

butler murdered Devon (p) maid is lying(q) gardenermurdered Devon (r) weapon was a slingshot(s) T T F F F F T T

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