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<Title><![CDATA[Logic Lesson 5 - Forms of Conditional Propositions]]></Title>
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<Title><![CDATA[Forms of Conditional Propositions]]></Title>
<Notes><![CDATA[Chapter 3   Section 4]]></Notes>
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<SlideText><![CDATA[Forms of Conditional Propositions Equivalent Propositions Chapter 3   Section 4 ]]></SlideText>
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<Title><![CDATA[Conditional Forms]]></Title>
<Notes><![CDATA[No in-class assignment problem]]></Notes>
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<SlideText><![CDATA[Conditional Forms Other translations for p ’! q, if p then q All p are q. p only if q. p is sufficient for q. p implies q. q is necessary for p. q, if p.  No in-class assignment problem ]]></SlideText>
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<Title><![CDATA[All squares are rectangles]]></Title>
<Notes><![CDATA[In-class Assignment 12 - 1]]></Notes>
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<SlideText><![CDATA[All squares are rectangles The different forms of this implication are listed below. If it is a square then it is a rectangle. Being a square implies it is a rectangle. It is a square  only if it is a rectangle. Being a square is sufficient for it to be a rectangle. It is a rectangle, if it is a square. Being a rectangle is necessary for it to be square. In-class Assignment 12 - 1 ]]></SlideText>
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<Title><![CDATA[Related Implications]]></Title>
<Notes><![CDATA[No in-class assignment problem]]></Notes>
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<SlideText><![CDATA[Related Implications Converse of p ’! q:     Switch p and q.     q ’! p Inverse of p ’! q:     Negate both p and q.     ~p ’! ~q Contrapositive of p ’! q:     Switch and negate both p and q.     ~q ’! ~p No in-class assignment problem ]]></SlideText>
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<Title><![CDATA[A number is divisible by 2, if it is even.]]></Title>
<Notes><![CDATA[In-class Assignment 12 - 2]]></Notes>
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<SlideText><![CDATA[A number is divisible by 2, if it is even. Recognize the form: q, if p p: It is even., ( The number is even.) q: a number is divisible by 2. (It is divisible by 2. If-then form:  If the number is even then it is divisible by 2. Converse:  If a number is divisible by 2 then it is even. Inverse:  If the number is not even then it is not divisible by 2. Contrapositive:  If the number is not divisible by 2 then it is not even.  In-class Assignment 12 - 2 ]]></SlideText>
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<Title><![CDATA[Propositions That Say the Same Thing]]></Title>
<Notes><![CDATA[No in-class assignment problem]]></Notes>
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<SlideText><![CDATA[Propositions That Say the Same Thing Propositions that say the same thing are equivalent. 2 symbolic propositions are equivalent if and only if under all possible conditions the truth value of one is the same as the truth value of the other. No in-class assignment problem ]]></SlideText>
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<Title><![CDATA[Check for Equivalency]]></Title>
<Notes><![CDATA[No in-class assignment problem]]></Notes>
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<SlideText><![CDATA[Check for Equivalency Write the given propositions in symbolic form. Make a truth table showing all conditions for both symbolic propositions. Check to see that the columns for the symbolic propositions are alike. No in-class assignment problem ]]></SlideText>
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<Title><![CDATA[p ’! q and ~p     q]]></Title>
<Notes><![CDATA[In-class Assignment 12   3, 4]]></Notes>
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<SlideText><![CDATA[p ’! q and ~p     q They are equivalent.  Therefore, every conditional may be written as a disjunction by negating the if component and changing the ’! to a disjunction sign. In-class Assignment 12   3, 4 ]]></SlideText>
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<Title><![CDATA[Writing Equivalent Propositions from Given Forms]]></Title>
<Notes><![CDATA[In-class Assignment 12 - 4]]></Notes>
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<SlideText><![CDATA[Writing Equivalent Propositions from Given Forms Given that ~q ’! p and q     p are equivalent forms.   Write an equivalent proposition to  June is a month of the year or 20 > 17. Determine in which of the 2 forms the given proposition is. The connective  or  says it is in the second form. Use the second form by using the negation of q and the  if   then  connective. Equivalent proposition:  If June is not a month of the year then 20 >17.    In-class Assignment 12 - 4 ]]></SlideText>
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<Title><![CDATA[De Morgan s Laws   Equivalent Propositions]]></Title>
<Notes><![CDATA[In-class Assignment 12 - 5]]></Notes>
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<SlideText><![CDATA[De Morgan s Laws   Equivalent Propositions De Morgan s Laws ~p    ~q ”! ~ (p     q) p: Sunday is not a weekday q: May is a month of the year Sunday is a weekday and May is not a month of the year.  It is not true that Sunday is not a weekday or May is a month of the year.   In-class Assignment 12 - 5 ]]></SlideText>
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<Title><![CDATA[De Morgan s Laws - continued]]></Title>
<Notes><![CDATA[In-class Assignment 12 - 5]]></Notes>
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<SlideText><![CDATA[De Morgan s Laws - continued 2. ~p    ~q ”! ~ (p     q) p: Sunday is not a weekday q: May is a month of the year Sunday is a weekday or May is not a month of the year.  It is not true that Sunday is not a weekday and May is a month of the year.   In-class Assignment 12 - 5 ]]></SlideText>
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<Title><![CDATA[Equivalent Statements]]></Title>
<Notes><![CDATA[In-class Assignment 12   6, 7]]></Notes>
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<SlideText><![CDATA[Equivalent Statements Write each proposition in its symbolic form.  Construct a truth table or recognize equivalent forms such as  De Morgan s Laws or an implication in its disjunction form.   In-class Assignment 12   6, 7 ]]></SlideText>
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