Test by Bikram | Mock GATE | Test 2 | Question: 8

Question

Suppose   $L =$ $\left \{ \right \}$ ,    $N = $$\left \{ 1,2,3 \right \}$

Now what does the set $N × L$ contain ?

• A.  $\left \{ \right \}$
• B. $\left \{ 1,2,3 \right \}$
• C. $\left \{ \left ( 1 \right )\left ( 2 \right ) \left ( 3 \right )\right \}$
• D. $\left \{ \left ( 3 \right )\left ( 2 \right ) \left ( 1 \right )\right \}$

Answer 1

Suppose A = {a, b} and B = {1, 2},

the set B × A will contain  { (1, a), (1, b), (2, 1), (2, b) }

However if either of the set in relation, let either A or B in B × A, is {  } or   it doesn’t contain any element, then the relation is also an empty set i.e. { }.

So, N * L is empty set means {  }  

= option A

Comments

sir what if one of them is
 { { } } or { Φ }

?

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The cartesian product is defined as $$A \times B = \{(a,b) \mid a\in A, b\in B\}.$$
In the case that one or both of the sets $A$ and $B$ are empty, there is no single index pair $(a,b)$ such that $a\in A$ and $b\in B$, which means $A\times B = \varnothing$.

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@Shaik Masthan

$\{\varnothing\}\times \{1,2\} = \{(\varnothing,1),(\varnothing,2)\}$, is this is true?

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@Lakshman Patel RJIT Sir, Is it? have you got the answer?