Suppose That $$g : A \rightarrow B \text { and } f : B \rightarrow C \text { where } A = B = C = \{ 1,2,3,4 \} , g =$$

question 73

Short Answer

suppose that $$g : A \rightarrow B \text { and } f : B \rightarrow C \text { where } A = B = C = \{ 1,2,3,4 \} , g =$$ $$\{ ( 1,4 ) , ( 2,1 ) , ( 3,1 ) , ( 4,2 ) \} \text {, and } f = \{ ( 1,3 ) , ( 2,2 ) , ( 3,4 ) , ( 4,2 ) \} \text {. }$$
- $$\text { Find } g \circ g \text {. }$$

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Definitions:

Modus Ponens

A form of deductive reasoning where, from premises in the form "If P, then Q" and "P", one concludes "Q".

Modus Tollens

A logical argument form that infers the denial of an antecedent from the denial of the consequent in a conditional statement.

Hypothetical Syllogism

A form of logical argument where two conditional statements lead to a conclusion if the first condition is true, then the conclusion follows.

Modus Ponens

A form of logical argument that concludes a certain consequent from a single premise in the form "If P, then Q" and P, therefore Q.