Tell whether each proposition is true, is false, or has unknown status at this time.

**kmjt** · September 22nd 2012, 01:46 PM

p is true
q is false
r's status is unknown at this time

Tell whether each proposition is true, is false, or has unknown status at this time.

q --> r (I know this would be true because if the hypothesis is false, the truth value is always true)

(p^r) <--> r (The textbook says the answer is true but how would I know this? All I know is that p is true, so if I don't know r it can be either true or false)

(q or r) <--> r (The textbook says this is true but I don't get how. All I know is q is false)

Please help

**Plato** · September 22nd 2012, 01:53 PM

Originally Posted by kmjt

p is true
q is false
r's status is unknown at this time

Tell whether each proposition is true, is false, or has unknown status at this time.
q --> r (I know this would be true because if the hypothesis is false, the truth value is always true)
(p^r) <--> r (The textbook says the answer is true but how would I know this? All I know is that p is true, so if I don't know r it can be either true or false)
(q or r) <--> r (The textbook says this is true but I don't get how. All I know is q is false)

$p \wedge r \Leftrightarrow r$ ia always true because if $r\equiv T$ both sides are true and if $r\equiv F$ both sides are false.

**kmjt** · September 22nd 2012, 06:02 PM

Originally Posted by Plato

$p \wedge r \Leftrightarrow r$ ia always true because if $r\equiv T$ both sides are true and if $r\equiv F$ both sides are false.

I do not quite understand

**Soroban** · September 22nd 2012, 06:23 PM

Hello, kmjt!

$p\text{ is true.}$
$q\text{ is false.}$
$r\text{ is either true or false.}$

Tell whether each proposition is true, is false, or has unknown status at this time.

$q \to r$
I know this would be true because if the hypothesis is false, the truth value is always true.
Right!

$(p\wedge r)\;\leftrightarrow\;r$
The textbook says the answer is true but how would I know this?
All I know is that p is true, so if I don't know r, it can be either true or false.

Since $p$ is true, we have: . $(T \wedge r)\;\leftrightarrow\;r$

If $r$ is true, we have: . $(T \wedge T) \leftrightarrow T \quad\Rightarrow\quad T \leftrightarrow T$

If $r$ is false, we have: . $(T \wedge F) \leftrightarrow F \quad\Rightarrow\quad F \leftrightarrow F$

$(q \vee r) \leftrightarrow r$
The textbook says this is true but I don't get how. All I know is q is false

Since $q$ is false, we have: . $(F \vee r) \;\leftrightarrow\; r$

If $r$ is true, we have: . $(F \vee T) \leftrightarrow T \quad\Rightarrow\quad T \leftrightarrow T$

If $r$ is false, we have: . $(F \vee F) \leftrightarrow F \quad\Rightarrow\quad F \leftrightarrow F$

Thread: Tell whether each proposition is true, is false, or has unknown status at this time.

LinkBack

Thread Tools

Display

Tell whether each proposition is true, is false, or has unknown status at this time.

Re: Tell whether each proposition is true, is false, or has unknown status at this ti

Re: Tell whether each proposition is true, is false, or has unknown status at this ti

Re: Tell whether each proposition is true, is false, or has unknown status at this ti

Similar Math Help Forum Discussions

Is the following claim true, false or sometimes true?

prove whether the set property is true, false, or sometimes true and sometimes false?

Prove whether the set property is always true, always false, or sometimes true or fal

True or False. Prove if true show counter example if false.

Propostions true, false, unknown

Search Tags