Class 12 Mathematics

Relation and Function

NCERT Exemplar Problems and Solution

NCERT Exemplar Problems-Long Answer-Part 4

Question: 25 - Functions NCERT Exemplar Problems and Solution class 12 Math (64) are defined respectively, by NCERT Exemplar Problems and Solution class 12 Math (65) find:

(i) fog

Solution:

NCERT Exemplar Problems and Solution class 12 Math (66)

(ii) gof

Solution:

NCERT Exemplar Problems and Solution class 12 Math (67)


(iii) fof

Solution:

NCERT Exemplar Problems and Solution class 12 Math (68)


(iv) gog

Solution:

NCERT Exemplar Problems and Solution class 12 Math (69)

Question: 26 – Let * be the binary operation defined on Q. Find which of the following binary operations are commutative.

NCERT Exemplar Problems and Solution class 12 Math (70)

Solution:

NCERT Exemplar Problems and Solution class 12 Math (71)

NCERT Exemplar Problems and Solution class 12 Math (72)

NCERT Exemplar Problems and Solution class 12 Math (73)

NCERT Exemplar Problems and Solution class 12 Math (74)



Question: 27 – Let * be binary operation defined on R by NCERT Exemplar Problems and Solution class 12 Math (75) Then the operation is:

(i) Commutative but not associative

(ii) associative but not commutative

(iii) neither commutative nor associative

(iv) both commutative and associative.

Answer: (i) is commutative but not associative.

Explanation:

NCERT Exemplar Problems and Solution class 12 Math (76)

Therefore, * is commutative.

NCERT Exemplar Problems and Solution class 12 Math (77)

Now, from equation (i) and (ii) it is clear that

NCERT Exemplar Problems and Solution class 12 Math (78)
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