Question

If the tire is flat, then I will have to change it. Using the statement above, first state your variables in terms of p and q and which variable represents which statement. Then write this statement in symbolic form.

a. p = tire is flat, q = change tire; Symbolic form: p→q
b. p = change tire, q = tire is flat; Symbolic form: q→p
c. p = tire is flat, q = don't change tire; Symbolic form: p→¬q
d. p = don't change tire, q = tire is flat; Symbolic form: ¬q→¬p

Answer 1

The statement 'If the tire is flat, then I will have to change it' can be symbolically represented as 'p → q', where 'p' stands for 'tire is flat' and 'q' stands for 'I will have to change the tire'.

Step-by-step explanation:

The given statement "If the tire is flat, then I will have to change it" can be represented using variables in symbolic logic.

First, we assign the variables:

• p = tire is flat,
• q = I will have to change the tire.

With these variables, the symbolic form of the statement is:

p → q

The arrow (→) denotes the logical connector 'implies'. So, if p is true (the tire is flat), then q must also be true (I will have to change it). This is a conditional statement, which is commonly used in logical arguments.