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Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Logic and True-False.

Let P,Q,R,S be four statements such that if P is true then Q is true, if Q is true then R is true and if S is true then at least one of Q and R is false then it follows that

- if S is false then both Q and R are true
- if at least one of Q and R is true then S is false
- if P is true then S is false
- if Q is true then S is true

Logic

Relations

True-False

But try the problem first...

Answer: if at least one of Q and R is true then S is false

Source

Suggested Reading

B.Stat Objective Question 65

Challenges and Thrills of Pre-College Mathematics by University Press

First hint

P true implies Q true and Q true imples R true

Second Hint

S true implies Q false with R false

Final Step

then R true implies Q true implies P true with S false then if at least one of Q and R is true then S is false.

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