I need help with some discrete
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I need help with some discrete

[From: ] [author: ] [Date: 13-02-20] [Hit: ]
To number 1, i believe the answer is infinite.And for number 3,1.2. {{1,......
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∈∅}

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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.
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