Evaluating Compound Propositions Section 1.2 Evaluating Compound Propositions

Vocabulary Words compound proposition

In-Class Activity #1 Get in groups of 3 or 4 students. By next week I’m going to ask you to try to settle into regular groups that you will use each day for the first half of the semester. Again, each person should print their name at the top of the paper I will hand out. As a group, complete Part One

Activity Let How would we write m = Juan is a math major c = Juan is a computer science major How would we write Juan is a math major but not a computer science major Juan is either a math major or a computer science major

Activity Let How would we write s = stocks are increasing i = interest rates are steady How would we write Stocks are increasing while interest rates are steady Neither are stocks increasing nor are interest rates steady

Activity Neither are stocks increasing nor are interest rates steady. It’s pretty common for me to hear several different answers for this one. How can we determine if two different answers are equivalent?

Truth Tables A truth table shows the relationship between various (often related) statements. It’s size depends on the number of independent variables represented in the statements N independent atomic formulae (variables)  2N rows

One possibility p q ¬ p  ¬ q T F

Order of Operations Just like there is an order of operations with arithmetic (remember PEMDAS?) there is an order of operation with logic. ¬  

One possibility p q ¬ p  ¬ q T F

One possibility p q ¬ p ¬ q ¬ p  ¬ q T F

Activity #2 Let’s see which variations are equivalent.

Variation 1 p q ¬ p ¬ q ¬ p  ¬ q T F

Variation 2 p q p  q ¬ (p  q) T F

Variation 3 p q p  q ¬ (p  q) T F

“Bigger” Compound Propositions While the examples we just looked at were “compound” because they had more than one operator, they still dealt with two variables. But lots of times when we use this phrase we are referring to three or more variables.

Activity #3 Let h = John is healthy w = John is wealthy s = John is wise

Activity #3 Write compound propositions representing John is healthy and wealthy but not wise John is not wealthy but he is healthy and wise John is neither healthy, wealthy, nor wise John is neither wealthy nor wise, but he is healthy. John is wealthy, but he is not both healthy and wise.

How do we build truth tables for these larger compound propositions?

Truth Tables A truth table shows the relationship between various (often related) statements. It’s size depends on the number of independent variables represented in the statements N independent atomic formulae (variables)  2N rows

A three variable truth table p q r p  q  r T F

Activity #4

A three variable truth table p q r p  (¬q  r ) T F

A three variable truth table p q r p  q  p  r T (1) F (2) (3) (4) (5) (6) (7) (8)