Question

Considere as seguintes afirmações sobre o conjunto U = {0,1,2,3,4,5,6,7,8,9}:

I) ∅ ∈ U e n(U) = 10.

II) ∅ ⊂ U e n(U) = 10.

III) 5 ∈ U e {5} ⊂ U.

IV) {0,1,2,5} ∩ {5} = 5.

Pode-se dizer, então, que é(são) verdadeira(s):

a) apenas I e III.

b) apenas II e IV.

c) apenas II e III.

d) apenas IV.

e) todas as afirmações.

Answer 1

Option e) all statements is correct

I) ∅ ∈ U and n (U) = 10. II) ∅ ⊂ U and n (U) = 10.

III) 5 ∈ U and {5} ⊂ U.

IV) {0,1,2,5} ∩ {5} = 5. are all true

Explanation:

Given that the set U = {0,1,2,3,4,5,6,7,8,9}

To find the statements which is true to the given universal set:

Given statements are I) ∅ ∈ U and n (U) = 10.

II) ∅ ⊂ U and n (U) = 10.

III) 5 ∈ U and {5} ⊂ U.

IV) {0,1,2,5} ∩ {5} = 5.

For :

A universal set is the collection of all elements in a particular manner.

All other sets are subsets of the universal set, the universal set is denoted by U.

Hence I) ∅ ∈ U and n (U) = 10.

II) ∅ ⊂ U and n (U) = 10.

III) 5 ∈ U and {5} ⊂ U.

IV) {0,1,2,5} ∩ {5} = 5. are all true by the definition of Universal set.

∴ Option e) all statements is correct