QUESTION FROM PRACTICE ASSIGNMENT

[HARSH BATRA]

PLEASE EXPLAIN , IN THIS CASE , HOW TO FIND CARDINALITY OF R3 ?

[HARSH BATRA]

[Debajyoti Biswas]

I guess this is from the last question of week 1 practice assignment. There R3 is defined as follows:

R3 = {(a, c) | a, c ∈ S, for some b ∈ S,(a, b) ∈ R1,(b, c) ∈ R2}. Please write the elements of R1, then write elements of R2, then find out which pairs of months will go in R3.  For example, for January, (Jan, Jan) ∈ R1, Now we assume three partitions in the set S, formed by the relation R2. These partitions are class 1, class 2, class 3. Hence from these classes, 7 pairs will be there in R3 starting with January. These are {(Jan, Jan), (Jan, Mar), (Jan, May), (Jan, July), (Jan, Aug), (Jan, Oct), (Jan, Dec)}. Moreover, (Jan, Feb) is in R1, and Feb is in another partition in S due to R2. So there are total 8 pairs (adding (Jan, Feb) with previous 7 elements) in R3 starting with Jan. 

Please check the practice assignment solution released, for further explanation.