Thinking Mathematically

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Thinking Mathematically

• 3.2 Compound Statements and Connectives

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Compound Statements
Simple statement conveys one idea. Examples
1. I have a dog.
2. I have a cat.
Compound statement combines two or more simple
statements. Examples
3. I have a dog and a cat.
4. I have a dog or a cat.
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Connectives

• Connectives are words used to combine statements

Name Word Used Example
I have a dog and a cat.
Conjunction
and
or
I have a dog or a cat.
Disjunction
If, then
If I have a dog, then I have a cat.
Conditional
if and only if
Biconditional
I have a dog if and only if I have a cat.
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Symbolic Logic

• Statements of Logic
• Name Symbolic Form In Words
• Negation p Not p
• Conjunction p/\q p AND q
• Disjunction p\/q p OR q
• Conditional p ? q IF p, THEN q
• Biconditional p? q p IF AND ONLY IF q

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• Examples
• Let p, q and r represent the following simple
  statements
• p It is raining.
• q It is not snowing.
• r I will go out.
• Write each compound statement in its symbolic
  form.
• a. It is raining and not snowing.
• b. It is raining and snowing.
• c. If it is raining, then I will go out.
• d. If I go out, then it is raining.
• e. If it is not raining, I will go out.
• f. If it is raining and snowing, then I will go
  out.

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• 2. Write each symbolic statement in words
• a. r ? p
• b. r ? (p /\ q)
• c. (r ? p) /\ q