Mathematics, 29.09.2019 03:30 uc22912

Show that (-91(pvp)) +n is a tautology (i. e. (91(pvp)) +7=t). (a) (3 points) show the equivalence using truth tables (b) (4 points) show the equivalence by establishing a sequence of equiv- alences. you can only use the equivalences in table 6 and the first equivalence in table 7. show your work by annotating every step.

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Answer from: Bellzers8328

The statement $(\lnot q \land(p\lor p))\rightarrow \lnot q$ is a tautology

Step-by-step explanation:

A tautology is a statement that is true for every assignment of truth values to its simple components.

a) A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

We have the statement $(\lnot q \land(p\lor p))\rightarrow \lnot q$ , which is compound by these statements:

$\lnot q$ $p\lor p$ $\lnot q \land(p\lor p)$

and we are going to use these simple statements to build the truth table.

The last column contains only true values. Therefore, the statement is a tautology.

b) We are going to use the table of logical equivalences as follows:

$(\lnot q \land(p\lor p))\rightarrow \lnot q \equiv$

$\equiv \lnot(\lnot q \land(p\lor p)) \lor \lnot q$ by the logical equivalence involving conditional statement.

$\equiv \lnot(\lnot q) \lor \lnot(p\lor p) \lor \lnot q$ by De Morgan's Law

$\equiv q \lor \lnot(p\lor p) \lor \lnot q$ by the Double negation law

$\equiv q \lor \lnot p \lor \lnot q$ by the Idempotent law

$\equiv (q \lor \lnot q)\lor \lnot p$ by Associative law

$\equiv T\lor \lnot p$ by Negation law

$\equiv T$ by Domination law

Show that (-91(pvp)) +n is a tautology (i.e. (91(pvp)) +7=t). (a) (3 points) show the equivalence us

Answer from: Quest

answer:

payment just for service

→

87.12

payment for service including tax

→

94.09

explanation:

service only with 20% tip

→

72.6

(

100

)

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the

service

−−−−−−

so technically the answer is

→

72.6

(

100

)

87.12

however, the intention of the question provider may have been that your answer is to be

87.12

(

100

)

94.09

to 2 decimal places.

payment just for service

→

87.12

payment for service including tax

→

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge

→

72.60

20% tip

100

72.60

14.52

−−−−−−

←

add

87.12

tax

100

87.12

6.97

−−−−−

←

add

94.09

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Show that (-91(pvp)) +n is a tautology (i. e. (91(pvp)) +7=t). (a) (3 points) show the equivalence u...