Question

Write the statements in symbolic form using the symbols

∼,∨
, and
∧
and the indicated letters to represent component statements. Either this polynomial has degree 2 or it has degree 3 but not both. (n = "This polynomial has degree 2," k = "This polynomial has degree 3")

Answer 1

(n∨k) ∧ ¬(n∧k)

Explanation:

We use three symbols, remember that

p∧q is true if and only if p is true and q is true

p∨q is true if and only if p is true or q is true

¬p is true if and only if p is false.

Now, to represent the statement "Either this polynomial has degree 2 or it has degree 3 but not both", the part "Either this polynomial has degree 2 or it has degree 3" can be written as "n∨k". The word "but" translates into "∧", and ""not both", means "not n∧k", that is, "¬(n∧k)". Hence the final proposition is (n∨k) ∧ ¬(n∧k)