Question

13. प्राकृतिक संख्याओं के समुच्चय में संबंध ‘से छोटा' है ।
The relation 'less than in the set of natural number is​

Answer 1

Answer:

The relation is transitive only.

Step-by-step explanation:

Consider the provided information.

Reflexive:

Let say "a, b and c" are the number which belongs to N.

$a,b,c \in N$

If we select a number "a", the number "a" can't be less than "a". As we know the number should be equal to itself.

For example if we take a=5 then 5 can't be less than 5, It will always equal to 5.

Since "a" is not less than "a" we can say that relation if not reflexive.

Symmetric:

If "a" is less than "b", it does not implies "b" is less than "a".

For example: Let a=5 and b=6

5<6 which is true but 6<5 is false.

Therefore, the relation is not symmetric.

Because for symmetric relation If (a, b) ϵ N then (b, a)ϵ N

Transitive:

Let us consider "a" is less than "b" and b is less than c this implies a is less than c is correct.

For example: Let a=5, b=6 and c=7

Here 5<6 and 6<7 that means 5<7

This is true

Since a is less than b and b is less than c

⇒ a is less than c.

Hence, the relation is transitive.

Answer 2

Answer:

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