Question

determine which, if any, of the three given statements are equivalent. you may use information about a conditional statements converse, inverse, or contrapositive, de morgans laws, or truth tables.
a. if he is flying, then his feet are not on the ground.
b. he is not flying or his feet are on the ground.
c. if he is not flying, then his feet are on the ground.
choose which statements are equivalent.
a. b and c
b. a and c
c. a and b
d. none of the statements are equivalent.

Explanation:

Step1: Define variables

Let \(p\) be "he is flying" and \(q\) be "his feet are on the ground". Then statement a is \(p
ightarrow
eg q\).

Step2: Rewrite statement b using logical equivalence

Statement b is \(
eg p\vee
eg q\). By the implication - disjunction equivalence \(p
ightarrow r=
eg p\vee r\), substituting \(r =
eg q\), we know \(p
ightarrow
eg q=
eg p\vee
eg q\). So a and b are equivalent.

Step3: Analyze statement c

Statement c is \(
eg p
ightarrow q\). Using the implication - disjunction equivalence \(
eg p
ightarrow q = p\vee q\), which is not equivalent to \(p
ightarrow
eg q\) or \(
eg p\vee
eg q\).

Answer:

C. a and b