P,Q, R are statements such that if P is true then at least one of the following is correct (i) Q is true (ii) R is not true then
if both Q and R are true then P is true
if both P and Q are true then R is true
if both P and R are true then Q is true
none of these
Key Concepts
Logic
Relations
True-False
Check the Answer
Answer: if both P and Q are true then R is true
B.Stat Objective Question 67
Challenges and Thrills of Pre-College Mathematics by University Press
Try with Hints
P true gives (i) holds and (ii) do not hold that is Q true and R true
P true gives (i) do not hold and (ii) holds that is Q non true and R non true
then from given conditions when P true and first condition holds that is Q true then second condition do not hold that is R is true that is if both P and Q are true then R is true.
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
Check the Answer
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
P true implies Q true and Q true imples R true
S true implies Q false with R false
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.
Relations and Numbers | B.Stat Objective | TOMATO 63
Try this TOMATO problem from I.S.I. B.Stat Objective based on Relations and Numbers.
Relations and Numbers (B.Stat Objective problems)
We consider the relation , "a person x shakes hand with a person y".Obviously if x shakes hand with y, then y shakes hand with x. In a gathering of 99 persons , one of the following statements is always true, considering 0 to be an even number, find which one is it.
there is at least one person who shakes hand with an odd number of persons
there is at least one person who shakes hand with an even number of persons
there are even number of persons who shake hand exactly with an even number of persons
none of these
Key Concepts
Logic
Relations
Numbers
Check the Answer
Answer: there is at least one person who shakes hand with an even number of persons
B.Stat Objective Question 63
Challenges and Thrills of Pre-College Mathematics by University Press
Try with Hints
Let R be handshakes among 99 persons holds
first person may handshake with at most 98(even) other persons, for second person similar arguments hold and this holds with similar arguments for all persons
then there exists at least one person who shakes hand with an even number of persons.
