Discrete Mathematics Assignment-5

a) False e.g.

b) True

​

​

c) False

​ e.g.

​ when

a) is a bijection

​

​ $\therefore x $ is a function

​ is an injection

​ is a surjection

​ is a bijection

b) is a function

​

​ $\therefore x $ is a function

​ is not an injection

​ is not a surjection

​ is not a bijection

c) is a bijection is a function

​

​ $\therefore x $ is a function

​ is an injection

​ is a surjection

​ is a bijection

d)f is a injection

​

​ $(((x_1,y_1) \in f \wedge (x_1,y_2)\in f) $ $\therefore x $ is a function

​ is a injection

​ is not a surjection

​ is not a bijection

a)

b)

c)

d)

a)

b)

c)

is a injection

$\because g: C\rightarrow A,h: C\rightarrow A $

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