If vs if and only if
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The document discusses the difference between "if" and "if and only if" statements. An "if" statement (A -> B) means that if A occurs, then B will occur. It does not mean B will only occur if A does, or that A is the only cause of B. An "if and only if" statement (A <-> B) means that A and B will occur together, and only together - if one occurs the other must also occur. Truth tables are provided to illustrate the logical differences between the two conditional statements. Examples are given to demonstrate their meanings.
If vs if and only if
- 1. If vs. if and only if By Aurora Computer Studies (auoracs.lk) 1
- 2. Overview • If (A -> B) • If and only if (A <-> B) Aurora Computer Studies 2
- 3. If A, then Q (A -> Q) 3
- 4. A -> Q - Meaning • A -> Q o If A happens then Q happens o A implies Q Aurora Computer Studies 4 A B C D . . P Q R . . Means : Other possibilities :
- 5. A -> Q - Truth table Aurora Computer Studies 5 A Q A->Q T T T T F F F T T F F T A B C D . . P Q R . .
- 6. A -> Q - What it means? • A -> Q o Yes, I mean; Whenever A happens Q happens (or high probability of Q happen) One of the reason for Q is A. Aurora Computer Studies 6 A B C D . . P Q R . .
- 7. A -> Q - What it does not means? • A -> Q o No, I do not mean; • A is the only reason(condition) for Q to happen • Whenever Q has happened means A has happened • If A happens, the only effect is Q happening Aurora Computer Studies 7 A B C D . . P Q R . .
- 8. A -> Q - Example 1 • If it rains, then the ground is wet Aurora Computer Studies 8 Rain B Watering D . . P Wet R . .
- 9. A -> Q - Example 2 • If you study, you can pass the assignment Aurora Computer Studies 9 Study B Cheat D . . P Pass R . .
- 10. if and only A, then Q (A <-> Q) 10
- 11. A <-> Q - Meaning • A <-> Q o If and only if A happens then Q happens o A -> Q and Q -> A Aurora Computer Studies 11 A . P Q R S Means : Other possibilities :
- 12. A <-> Q - Truth table Aurora Computer Studies 12 A Q A->Q T T T T F F F T F F F T A . P Q R S
- 13. A <-> Q - What it means? • A <-> Q o Yes, I mean; Whenever A happens Q happens Only when A happens Q happens If Q has happened, then A must have happened Aurora Computer Studies 13 A . P Q R S
- 14. A <-> Q - What it does not means? • A <-> Q o No, I do not mean; • If A happens then, only Q happens Aurora Computer Studies 14 A . P Q R S
- 15. A <-> Q - Example 1 • If and only if the offence is proved, then accused is declared guilty Aurora Computer Studies 15 Prove the offence . P Guilty Punish S
- 16. A <-> Q - Example 2 • If and only if you understand, then you can solve this problem Aurora Computer Studies 16 Understand . P Solve Happy S
- 17. Thank You ! Presented by Aurora Computer Studies (auoracs.lk) Aurora Computer Studies 17
- 18. "We are what we repeatedly do. Excellence, then, is not an act, but a habit." ~ Aristotle. Aurora Computer Studies 18
- 19. For more resources visit; http://www.slideshare.net/auroracslk Aurora Computer Studies 19
- 20. Contact Information Premier Study Center Aurora Computer Studies, Summerset College, # 135, 3rd Floor, DFCC Building, High Level Road, Maharagama. 0115 690 290 City Study Center Aurora Computer Studies, Summerset College, # 88/2, 2nd Floor, BOC Building, High Level Road, Kirulapone, Colombo 06 0703 001 010 For further details and enquiries : Call - 0719 842030 E-mail – info@auroracs.lk Web - www.auroracs.lk 20