• Wayne Wigfield’s answer is quite right and his example is very helpful. I only offer a bit of clarification and some precision. The concepts of inverse, converse, and contrapositive refer specifically to forms of conditional assertions or proposit...
• This packet will cover "if-then" statements, p and q notation, and conditional statements including contrapositive, inverse, converse, and biconditional. Use this packet to help you better understand conditional statements.
• ment is called the converse of the statement in the preceding example. In Chapter 7, we will have more to say about the converse of a condi-tional statement; we’ll also cover two related statements called the inverse and contrapositive. Of these, only the contrapositive is equivalent to the orig-inal conditional.
• Validating the statements involving the connecting words – difference between contradiction, converse and contrapositive, Mathematical induction; Linear Inequalities, solution of linear inequalities in one variable (Algebraic) and two variables (Graphical).
• Step 2. Rewrite this statement in the contrapositive form: ∀ x ∈ D, if Q(x) is false, then P(x) is false. Step 3. Prove the contrapositive statement by direct proof: 3a. Suppose x is a [particular but arbitrarily chosen] element of D such that Q(x) is false. 3b. Show that P(x) is false.
• Write the converse, inverse, and contrapositive of each statement. 5. Ifyou like hockey, then you goto the hockey game. 6. Ifx is odd, then 31 is odd. Created Date:
\$\begingroup\$ @SantiagoCanez I suppose you can phrase the proof that way, but it can also be phrased as a contradiction proof. In particular, you can certainly find lots of books written by perfectly good mathematicians in which the proof is described as a proof by contradiction.
• Contrapositive p Æq is another conditional statement ~q Æ~p • A conditional statement is equivalent to its contrapositive • The converse of p Æq is q Æp • The inverse of p Æq is ~p Æ~q • Conditional statement and its converse are not equivalent • Conditional statement and its inverse are not equivalent
Using the Contrapositive Equivalence in Proofs The contrapositive ofa conditional statement is formed by interchanging its LHS with its RI-IS, and negating both sides ofthe new implication. In Statement 5. —p vs Reason Premise Contrapositive Equivalence (1) Premise Modus Tollens (2) (3) Disjunctive Addition (4) Premise Modus Ponens (5) (6) This will include identifying the converse, inverse, and contrapositive of a conditional statement; G.1b The student will use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion.
14 Logic II: Converse and contrapositive Another important piece of logic in theoretical math is the relationship among an if-then statement, its converse, and its contrapositive. The converse of the statement “If P, then Q” is “If Q, then P.”
Inductive vs. deductive reasoning. While deductive reasoning proceeds from general premises to a specific conclusion, inductive reasoning proceeds from specific premises to a general conclusion. While deductive reasoning is top-down logic, inductive reasoning is sometimes referred to as bottom-up logic. Converse, Inverse and Contrapositive of the statement 1.4 Q.4 Miscellaneous Q.19, 21 Using Quantifiers Convert Open sentences into True statement 1.6 Q.2 Prepare the Truth Table/Find Truth Values of p and q for given cases 1.4 Q.7 1.5 Q.1 Miscellaneous Q. 12, 15 Examine the statement Patterns (Tautology, Contradiction,
Note also that: • When two statements must be either both true or both false, they are called equivalent statements. o The original statement and the contrapositive are equivalent statements. o The converse and the inverse are equivalent statements. And this can be seen by realizing that the MN of a statement, and the MR of that same original statement, are actually contrapositives of each other. As we know, a statement and its contrapositive are fundamentally identical, and so a Mistaken Negation and a Mistaken Reversal are really the same basic idea expressed in different ways.