Question

In each represent the common form of each argument using letters to stand for component sentences, and fill in the blanks so that the argument in part (b) has the same logical form as the argument in part (a).

a. If all integers are rational, then the number 1 is rational.
All integers are rational.
Therefore, the number 1 is rational.

b. If all algebraic expressions can be written in prefix notation, then ____________________ .

Therefore, (a+2b)(a2-b) can be written in prefix notation.

Answer 1

(a+2b)(a2-b) can be written in prefix notation.

Explanation:

In this problem, the data presented in item b. must follow the same logical form as item a.

Iteam a. follows an "if... then...therefore" structure

let x and y be logical statements, the logical structer is:

"if x, then y. Therefore y."

Applying it to item b:

"If all algebraic expressions can be written in prefix notation, then _______

Therefore, (a+2b)(a2-b) can be written in prefix notation."

In this case, x = "all algebraic expressions can be written in prefix notation" and y = "(a+2b)(a2-b) can be written in prefix notation."

Filling in the blank accordingly gives us:

"If all algebraic expressions can be written in prefix notation, then (a+2b)(a2-b) can be written in prefix notation.

Therefore, (a+2b)(a2-b) can be written in prefix notation."