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Could anybody help me check whether my judgements ture or false? (MJ = My Judgement)

Suppose f maps A into B, and g maps B into C

1. If f and g are injective, then g[tex]\circ[/tex]f is injective;

(MJ)but that when g[tex]\circ [/tex]f is injective, the injectivity of f and g are unsure.

2. If f and g are surjective, then g[tex]\circ[/tex]f is surjective;

(MJ)and that when g[tex]\circ[/tex]f is surjective, f and g are both surjective.

Thx!

Suppose f maps A into B, and g maps B into C

1. If f and g are injective, then g[tex]\circ[/tex]f is injective;

(MJ)but that when g[tex]\circ [/tex]f is injective, the injectivity of f and g are unsure.

2. If f and g are surjective, then g[tex]\circ[/tex]f is surjective;

(MJ)and that when g[tex]\circ[/tex]f is surjective, f and g are both surjective.

Thx!

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