Cartesian Product

Question

Suppose   L = { {}  } ,    N = {1, 2, 3}.

Now what does the set N × L contain ?

Comments

I think,

If N = {{}} then prooduct will be {(1,{}) , (2,{}) , (3,{})}

If N = {} then product will be {}.

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N x L = { (1, {}) , (2, {}) (3, {}) }.

Here L is not $\varnothing$. It is set containing one element and that element is $\varnothing$.

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yes, 3 elements in cartesian product

Answer 1

Cardinality of N is 3

Cardinality of L is 1

Cardinality of N X L is 3.

using this 

   {1, 2, 3} X { {} } =>  { (1, {}) , (2, {}) (3, {}) }

Please note L is not phi it is having one element here. The set {{}} or

{∅}contains one element.