Problem sets

Part I:

1. Write 3 examples of a valid statement in symbolic or set logic

• 1_________________
• 2_________________
• 3_________________

2. Consider the following logic statements:

• p: Manila is the capital of the Philippines
• q: Today is Friday
• r: The weather is bad today

Write the following logic statements according to the operations:

• ?p
• p?q
• q?r
• p??q
• q?r
• r?q

Part II:

3. Consider the following statements

• p: It's cold outside
• q: The water heater is not working
• r: We need to wear face mask

Translate the following symbolic statement to verbal form

1. (p?q)??r(p?q)??r
2. ?p?(q?r)?p?(q?r)
3. ?r?p?r?p
4. r?(p?q)r?(p?q)

Part III:

4. Complete the following TRUTH TABLES:

\f~p q P ~p ~p A q T T T F F T F F\f~ p A ~ q p q ~P ~ q ~ p A ~ q T T T F F T F F