The mini-lesson targeted the fascinating concept of the conditional statement. Write the converse, inverse, and contrapositive statements and verify their truthfulness. The contrapositive statement is, "If you did not pass the exam, then you did not study well" (if not q, then not p).Ģ. If 2a + 3 < 10, then a = 3. The inverse statement is, "If you do not study well then you will not pass the exam" (if not p, then not q). The converse statement is, "You will pass the exam if you study well" (if q, then p). The given statement is - If you study well, then you will pass the exam. If you study well, then you will pass the exam. Write the converse, inverse, and contrapositive statement for the following conditional statement. Thus the condition is true.Ģ4 is not divisible by 9. Thus, the conclusion is true.Ĭ) 24 is a multiple of 3. Thus, the condition is true.Ģ7 is divisible by 9. Thus, the conclusion is false.ī) 27 is a multiple of 3. Thus, the condition is false.ġ6 is not divisible by 9. Let us find whether the conditions are true or false.Ī) 16 is not a multiple of 3. Do you agree or disagree? Justify your answer.Ĭonditional statement: If a number is a multiple of 3, then it is divisible by 9. Joe examined the set of numbers to check if they are the multiples of 3. Which of the following could be the counterexamples? Justify your decision.Ī) A rectangle with sides measuring 2 and 5ī) A rectangle with sides measuring 10 and 1Ĭ) A rectangle with sides measuring 1 and 5ĭ) A rectangle with sides measuring 4 and 3Ī) Rectangle with sides 2 and 5: Perimeter = 14 and area = 10ī) Rectangle with sides 10 and 1: Perimeter = 22 and area = 10Ĭ) Rectangle with sides 1 and 5: Perimeter = 12 and area = 5ĭ) Rectangle with sides 4 and 3: Perimeter = 14 and area = 12 Ray tells "If the perimeter of a rectangle is 14, then its area is 10." There are four types of conditional statements: Identify the types of conditional statements. ![]() Let us have a look at a few solved examples on conditional statements. Observe the truth table for the statements:Īccording to the table, only if the hypothesis (A) is true and the conclusion (B) is false then, A → B will be false, or else A → B will be true for all other conditions. Let us hypothetically consider two statements, statement A and statement B. Thus, we have set up a conditional statement. The 'then' part is that the number should be even.'If' part is a number that is a perfect square.If a number is a perfect square, then it is even. Here, the point to be kept in mind is that the 'If' and 'then' part must be true. ![]() Here the conditional statement logic is, A if and only if B (A ↔ B) The statement is a biconditional statement when a statement satisfies both the conditions as true, being conditional and converse at the same time.īiconditional : “Today is Monday if and only if yesterday was Sunday.” Here the conditional statement logic is, if not B, then not A (~B → ~A) Biconditional Statement When the hypothesis and conclusion are negative and simultaneously interchanged, then the statement is contrapositive.Ĭontrapositive: “If yesterday was not Sunday, then today is not Monday” Here the conditional statement logic is, If not A, then not B (~A → ~B) Contrapositive Statement Inverse: “If today is not Monday, then yesterday was not Sunday.” When both the hypothesis and conclusion of the conditional statement are negative, it is termed as an inverse of the statement.Ĭonditional Statement:“If today is Monday, then yesterday was Sunday”. Here the conditional statement logic is, If B, then A (B → A) Inverse of Statement When hypothesis and conclusion are switched or interchanged, it is termed as converse statement.Ĭonditional Statement: “If today is Monday, then yesterday was Sunday.”Ĭonverse: “If yesterday was Sunday, then today is Monday.” Let us consider hypothesis as statement A and Conclusion as statement B. To check whether the statement is true or false here, we have subsequent parts of a conditional statement. On interchanging the form of statement the relationship gets changed. Let us consider the above-stated example to understand the parts of a conditional statement.Ĭonditional Statement: If today is Monday, then yesterday was Sunday. Hypothesis (if) and Conclusion (then) are the two main parts that form a conditional statement. ![]() What Are the Parts of a Conditional Statement? Here are two more conditional statement examplesĮxample 1: If a number is divisible by 4, then it is divisible by 2.Įxample 2: If today is Monday, then yesterday was Sunday. '\(\rightarrow\)' is the symbol used to represent the relation between two statements. For example, A\(\rightarrow\)B. Here 'p' refers to 'hypothesis' and 'q' refers to 'conclusion'.įor example, "If Cliff is thirsty, then she drinks water." What Is Meant By a Conditional Statement?Ī statement that is of the form "If p, then q" is a conditional statement.
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