Questions: Consider statements p, q, and r. p: It is Tammy's birthday. q : We are having pizza for dinner. r : It is May. For each part below, fill in the symbolic form. Descriptive form (a) It is not Tammy's birthday, and it is May or we are having pizza for dinner. (b) It is not May and it is Tammy's birthday, if and only if we are not having pizza for dinner. Symbolic form

Consider statements p, q, and r.
p: It is Tammy's birthday.
q : We are having pizza for dinner.
r : It is May.
For each part below, fill in the symbolic form.

Descriptive form
(a) It is not Tammy's birthday, and it is May or we are having pizza for dinner.
(b) It is not May and it is Tammy's birthday, if and only if we are not having pizza for dinner.

Symbolic form

Transcript text: Consider statements $p, q$, and $r$. p: It is Tammy's birthday. $q$ : We are having pizza for dinner. $r$ : It is May. For each part below, fill in the symbolic form. Descriptive form (a) It is not Tammy's birthday, and it is May or we are having pizza for dinner. (b) It is not May and it is Tammy's birthday, if and only if we are not having pizza for dinner. Symbolic form $\square$ $\square$

Solution

Solution Steps

Solution Approach

To convert the given descriptive statements into symbolic form, we need to use logical operators. For statement (a), we use the logical operators for "not" (¬), "and" (∧), and "or" (∨). For statement (b), we use "not" (¬), "and" (∧), and "if and only if" (↔).

Step 1: Define the Statements

We define the following statements:

$ p $: It is Tammy's birthday.
$ q $: We are having pizza for dinner.
$ r $: It is May.

Step 2: Convert Descriptive Form to Symbolic Form

For the first statement:

(a) "It is not Tammy's birthday, and it is May or we are having pizza for dinner." can be expressed symbolically as: \[ ¬p ∧ (r ∨ q) \]

For the second statement:

(b) "It is not May and it is Tammy's birthday, if and only if we are not having pizza for dinner." can be expressed symbolically as: \[ ¬r ∧ p ↔ ¬q \]