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# Logic and True-False | B.Stat Objective | TOMATO 65

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

## Logic and True-False (B.Stat Objective problems)

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

### Key Concepts

Logic

Relations

True-False

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

B.Stat Objective Question 65

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

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.