Write each of these propositions in the form "p if and only if q" in English. a) If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside.
b) For you to win the contest it is necessary and sufficient that you have the only winning ticket.
c) You get promoted only if you have connections, and you have connections only if you get promoted.
d) If you watch television your mind will decay, and conversely.
e) The trains run late on exactly those days when I take it.

The "p if and only if q" statement is equivalent to "q if and only if p", then let's rewrite all the propositions in this way.

a) "If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside."

We can define:

q = is hot outside

p = you buy an ice cream cone

Then we can rewrite this as:

"You buy an ice cream cone if and only if is hot outside"

b)  "For you to win the contest it is necessary and sufficient that you have the only winning ticket."

We can define:

p = you winning the contest

q = have the winning ticket

Then we can rewrite (changing some words) this as:

"You will win the contest if and only if you have the winning ticke"

c) "You get promoted only if you have connections, and you have connections only if you get promoted."

We can define:

p = you get promoted

q = you have connections

We can rewrite the proposition as:

"You can get promoted if and only if you have connections"

d) " If you watch television your mind will decay, and conversely."

We can define:

p = you watch television

q = your mind will decay

We can rewrite it as:

"You can watch television if and only if your mind decays"

e) " The trains run late on exactly those days when I take it."

We can define:

p = The train runs late

q = I take it.

We can rewrite the proposition as:

"The train runs late if and only if I take it"

the reporter's right

step-by-step explanation:

1/4 = .25 / 25%

step-by-step explanation:

given expression is .

now we need to simplify the given expression .

we know that square root is equivalent to the power 1/2. so that means we can take half of the exponents to get the square root of given expression.

expanding that will give a very very large number so let's keep answer in exponent form.