Logic Statements:Conditional statements
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Conditional statements relate a hypothesis and conclusion with an "if-then" structure. A conditional statement is false if the hypothesis is true but the conclusion is false. Some examples of conditional statements and their truth values are provided, including: - If LJ rests for 10 days, then his ankle will heal. This would be false if LJ rested 10 days but his ankle did not heal. - If x is prime, then x is odd. This is false because 2 is prime but not odd. - If I study, then I will pass the exam. This would be false if I studied but still failed the exam.
Logic Statements:Conditional statements
- 1. LOGIC STATEMENTS MARIELE BRUTAS Ateneo de Naga University, Philippines
- 2. Statement is a declarative sentence that is either TRUE or FALSE.
- 3. Examples:
- 4. CONDITIONAL STATEMENTS Conditional Statements are combinations of statements in an If - then structure. A statement in this form has two parts. The phrase immediately following the word If is the hypothesis and the phrase immediately following the word then is the conclusion.
- 5. Identify the hypothesis and the conclusion in each statement. If it rains, then the ground is wet. If a polygon is a nonagon, then it has 9 sides. If an animal is a tiger, then it is a mammal.
- 6. Write each statement in its conditional form. Dogs have four legs. If an animal is a dog, then it has four legs. Parallelograms have two pairs of parallel sides. If a figure is a parallelogram, then it has two pairs of parallel sides. Parallel lines do not intersect. If two lines are parallel, then they do not intersect.
- 7. When is a conditional statement true? When is it false?
- 8. Statement: If I do my homework, then I get my allowance. I did my homework, and I got my allowance. The hypothesis is true and the conclusion is true. Answer: Since what was expected happened, therefore the conditional statement is TRUE.
- 9. Statement: If I do my homework, then I get my allowance. I did not do my homework, and I did not get my allowance. The hypothesis is false, the conclusion is false. Answer: Since it was not stated what will happen if I do not do my homework, then the statement cannot be false. Therefore it’s TRUE.
- 10. Statement: If I do my homework, then I get my allowance. I did not do my homework, I still got my allowance. The hypothesis is false, the conclusion is true. Answer: Since it was not stated what will happen if I do not do my homework, then the statement cannot be false. Therefore it’s TRUE.
- 11. Statement: If I do my homework, then I get my allowance. I did my homework, but I did not get my allowance. The hypothesis is true, the conclusion is false. Answer: Since the result is not what was expected, therefore the statement is FALSE.
- 13. THEREFORE, a conditional statement is false if you can give a case when the hypothesis is true and the conclusion is false.
- 14. When is each statement false given that the hypothesis is true? 1. If LJ will rest for 10 days, then his ankle will heal. LJ rests for 10 days, but his ankle still hurts. 2. If x is prime, then x is odd. 2 is prime but is not odd. 3. If I study, then I will pass the exam. I studied but still failed the exam.