Logic Puzzles

27. Logical Deduction with Variables

Given the statements: P and Q (Q or R), if P then S, not S, if R then A, not A. What can you conclude?

Added 20 June 2011

Solution:

From the statements, we have:

  • P and Q (Q or R)
  • If P then S
  • Not S
  • If R then A
  • Not A

Since 'if P then S' and 'not S', we conclude 'not P'.

From 'P and Q (Q or R)', if 'not P', then 'Q or R' must be true.

Since 'if R then A' and 'not A', we conclude 'not R'.

Therefore, R must be false.


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