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Conditional and Biconditional Statements
Laws of Syllogism and Detachment
100
Identify the hypothesis and conclusion of the conditional statement. If I answer a phone call, then I have a phone.
The hypothesis is if I answer a phone call. The conclusion is then I have a phone.
100
Determine if the conjecture is valid by the Law of Detachment. Given: If Sue buys a TV, then Sue must have money. Sue has money. Conjecture: Sue bought a TV.
Invalid.
200
Write a conditional statement from the following fact. A dog has fur.
If it is a dog, then it has fur.
200
Determine if the conjecture is valid by the Law of Syllogism. Given: If you are in Lansing, then you are in Michigan. If you are in Michigan, then you are in the USA. Conjecture: If you are in Lansing, then you are in the USA.
Valid
300
Write the defenition as a biconditional. An acute angle is an angle whose measure is less than 90 degrees.
It is an acute angle iff its measure is less than 90 degrees.
300
Determine whether the conjecture is valid by the Law of Detachment. Given: If Nancy makes dinner, then Nancy must have food. Nancy makes dinner. Conjecture: Nancy has food.
Valid.
400
Define inverse, converse, contrapositive, negation, and truth value.
The inverse is the statement formed by negating the hypothesis and conclusion. The converse is the statement formed by exchanging the hypothesis and conclusion. The contrapositive is the statement formed by negating and exchanging the hypothesis and conclusion. Negation is the contradiction of a statement using "not." The truth value of a statement is either true (T) or false (F).
400
Determine whether the conjecture is valid by the Law of Syllogysm. Given: If it is a square, then it is a rectangle. If it is a rectangle, then it is a polygon. Conjecture: If it is a polygon, then it is a square.
Invalid
500
Write the converse, inverse, contrapositive, and truth value for the following conditional statement. If it is a cat, then it has a tail.
The inverse is if it is not a cat, then it has no tail (F). The converse is if it has a tail, then it is a cat (F). The contrapositive is if it has no tail, then it is not a cat (T).
500
Determine whether the conjecture was reached using the Law of Syllogism or Detachment. Given: If it is a square, then it is a diamond. ADFG is a square. Conjecture: ADFG is a diamond.
Law of Detachment