Answer to Question #291505 in Discrete Mathematics for Arjun

Question #291505

Let A = {x € N: 3 ≤ x ≤ 13}, B = {x € N : x is even}, and C = {x EN: x is odd}.



(a) Find An B.



(b) Find A UB.



(c) Find Bn C..



(d) Find BUC.

1
Expert's answer
2022-01-30T16:38:14-0500

We are given that,

A=xN:3x13,B=xN:x is even,and C=xN:x is odd.A = {x \in \N: 3 ≤ x ≤ 13}, B = {x \in \N : x\space is \space even}, and\space C = {x \in \N: x\space is\space odd}.  

then,

A={3,4,5,6,7,8,9,10,11,12,13}B={2,4,6,8,...}C={1,3,5,7,9,......}A=\{3,4,5,6,7,8,9,10,11,12,13\}\\B=\{2,4,6,8,...\}\\C=\{1,3,5,7,9,......\}


a)a)

ABA\cap B consist of the elements common to both set AA and set BB.

Therefore,

AB={4,6,8,10,12}A\cap B=\{4,6,8,10,12\}  


b)b)

ABA\cup B consist of all elements in set AA and set BB.

Therefore,

AB={2,3,4,5,6,7,8,9,10,11,12,13,14,16,18,20,.....}A\cup B=\{2,3,4,5,6,7,8,9,10,11,12,13, 14,16,18,20,.....\}

For this case, ABA\cup B consist of all even numbers and the odd numbers, 3,5,7,9,11,13 in set AA.


c)c)

BCB\cap C  consist of elements common to both set B and set C. Clearly, BC={}.B\cap C=\{\empty\}. This is because, no element is common to both sets as set B consist of all even numbers and set C consist of all odd numbers. A number can either be even or odd.


d)d)

BCB\cup C consist of all elements in set B and set C.

Therefore,

BC={1,2,3,4,5,6,7,8,9,10,11,12,13,...}B\cup C=\{1,2,3,4,5,6,7,8,9,10,11,12,13,...\}. We can observe that this is the set  of natural numbers(N)(\N) .  


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