I somewhat understand these but I just want to make sure.
I think the answer to number 2 is 5.
To number 1, i believe the answer is infinite.
And for number 3, i think it is 0
Find the cardinality of these sets
1. {x∈ Z; ∅⊆{x}}
2. {{1,2},{3,4,5}}
3. {x∈ Z;x∈∅}
I think the answer to number 2 is 5.
To number 1, i believe the answer is infinite.
And for number 3, i think it is 0
Find the cardinality of these sets
1. {x∈ Z; ∅⊆{x}}
2. {{1,2},{3,4,5}}
3. {x∈ Z;x∈∅}
-
1 is countably infinite, so you're probably close enough for your class
3 is indeed 0, there are no elements in the empty set so no elements in this set
2 is however 2. Notice that the big set contains as elements two smaller sets x = {1,2} and y = {3,4,5}. So we have {{1,2}, {3,4,5}} = {x,y} and now it's easier to see that this has cardinality 2. If a set has sets as elements, the cardinality of the largest outside set is NOT the sum of the cardinalities of the element sets, but just the number of them.
3 is indeed 0, there are no elements in the empty set so no elements in this set
2 is however 2. Notice that the big set contains as elements two smaller sets x = {1,2} and y = {3,4,5}. So we have {{1,2}, {3,4,5}} = {x,y} and now it's easier to see that this has cardinality 2. If a set has sets as elements, the cardinality of the largest outside set is NOT the sum of the cardinalities of the element sets, but just the number of them.