Question

A die is tossed twice and the number of dots facing up is counted and noted in the order of occurrence. let us define a ∶ total number of dots showing is even b ∶ both dice are even c ∶ number of dots in dice differ by 1 (i) does a imply b or does b imply b? (ii) find a ∩

c.

Answer 1

Given : A die is tossed twice and the number of dots facing up is counted and noted in the order of occurrence

A ∶ Total number of dots showing is even

B ∶ Both dice are even

C ∶ Number of dots in dice differ by 1

To Find : Does A imply B or does B imply A

A ∩ C.

Solution:

Dots in dice  1 can be from 1 to 6

Dots in Dice 2  can be from 1 to 6

Total number of dots showing is even

A= { ( 1 , 1) , ( 1 , 3) , ( 1 , 5) , ( 2 , 2) , ( 2 , 4) , ( 2 , 6) , ( 3 , 1) , (3 , 3) , ( 3  5) , ( 4 , 2) , ( 4 , 4) , ( 4, 6) , ( 5 ,1 ) , ( 5 , 3) , ( 5 , 5) , ( 6 , 2) , ( 6 , 4) , ( 6 , 6) }

B ∶ Both dice are even

=> B = { (2 , 2) , ( 2 , 4) , ( 2  6) , ( 4 , 2) , ( 4 , 4) , ( 4 , 6) , (6, 2) , (6 ,4 ) , (6 , 6) }

B ⊂ A

Hence B implies A

A Does not imply B

Number of dots in dice differ by 1

C = { ( 1 , 2) , ( 2 , 1 ), (2 , 3) , ( 3 , 2) , ( 3 , 4) , ( 4 ,3 ) , ( 4 , 5) , ( 5 , 4) , (5, 6)  ,(6 , 5) }

A ∩ C = {} = Ф

as A has difference of 0 , 2 or  4  while C has difference of 1

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