) Let A be the set of natural numbers less than 6 and whose greatest common divisor with 6 is 1. Let B be the set of divisors of 6. What are the cardinalities of A, B, A ∪ B and A ∩ B?
Answers
Answer:
(2,4,5,1)
Step-by-step explanation:
A= {1,5} >
b={1,2,3,6}
Hence cardinality of
|A| = 2
|B| = 4
|AUB| ={1,2,3,5,6} = 5
|A∩B| = {1}= 1
Given : A is the set of natural numbers less than 6 and whose greatest common divisor with 6 is 1.
B is the set of divisors of 6.
To Find : What are the cardinalities of A, B, A ∪ B and A ∩ B
Solution:
Natural numbers less than 6 are 1 , 2 , 3 , 4 , 5
Greatest common divisor with 6 is 1
are 1 , 5 as 2 , 3 and 4 has common factors greater than 1 with 6
A = { 1 , 5 }
B is the set of divisors of 6.
B = { 1 , 2 , 3 , 6 }
Cardinality of set is number of elements in the set
A = { 1 , 5 }
=> n(A) = 2 Hence Cardinality of A is 2
B = { 1 , 2 , 3 , 6 }
=> n(B) = 4 Hence Cardinality of B is 4
A U B = { 1 , 2 , 3 , 5 , 6 }
n ( A U B) = 5
=> Cardinality o A U B is 5
A ∩ B = { 1 }
n ( A ∩ B) = 1
=> Cardinality of A ∩ B is 1
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