Question

For this Discussion, follow these three steps:

Answer 1

Part 1: "If it rains, then there are clouds"

a) "it rains"

b) "there are clouds"

c) true.

d) "if there are clouds, then it rains"

e) false.

Part 2: "If a number is larger than 5, then the number is larger than 3"

a)  "a number is larger than 5"

b)  "a number is larger than 3"

c) true

d) "If a number is larger than 3, then it is larger than 5"

e) False

Part 3: ""A number is even if and only if it is a multiple of 2""

a) true.

What is a conditional statement?

For two propositions P and Q, a conditional statement is:

If P then Q.

Part 1:

A conditional statement is:

"If it rains, then there are clouds"

a) The hypothesis is the first proposition, which is "it rains"

b) The conclusion is the second proposition "there are clouds"

c) The statement seems to be true, as the rain comes from the clouds, so it seems to be true.

d) The converse statement is:

"If Q then P"

In this case, it would be:

"If there are clouds, then it rains"

e) That statement is clearly false, because not always that there are clouds in the sky there is rain.

Part 2.

Another conditional statement could be:

"If a number is larger than 5, then the number is larger than 3"

a) The hypothesis is "a number is larger than 5"

b) The conclusion is "a number is larger than 3"

c) The statement is true because 5 is larger than 3, then if a number is larger than 5 it must be larger than 3.

d) The converse statement is:

"If a number is larger than 3, then it is larger than 5"

e) Which is clearly false, a counterexample is 4, which is larger than 3 but not larger than 5.

Part 3.

A biconditional statement is:

P if and only if Q.

One example is:

"A number is even if and only if it is a multiple of 2"

a) That statement is clearly true, as that is the definition of an even number.

If you want to learn more about conditional statements:

brainly.com/question/18152035

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