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19 votes
19 votes
  • If either wages or prices are raised, there will be inflation.
  • If there is inflation, then either the government must regulate it or the people will suffer.
  • If the people suffer, the government will be unpopular.
  • Government will not be unpopular.

Which of the following can be validly concluded from the above statements.

  1. People will not suffer
  2. If the inflation is not regulated, then wages are not raised
  3. Prices are not raised
  4. If the inflation is not regulated, then the prices are not raised
  5. Wages are not raised
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5 Answers

Best answer
19 votes
19 votes
It is told in the question "If the people suffer, the government will be unpopular". And "government will not be unpopular" means, people will not suffer.
It is like $A \rightarrow B$ is true and ~B is given. So, ~A must be true.

So, (A) is valid (always true).

Lets take the English meaning

Government will not be unpopular

$\implies$ People will not suffer
$\implies$ Either no inflation or government regulates it
$\implies$ If no regulation then no inflation
$\implies$ if no regulation then no wage or price rise

So, (B) and (D) are valid (always true) and (C) and (E) are not valid.
edited by
4 votes
4 votes

let the variable we use are 
W : wages are raised
P : prices are raised
I :  there is inflation
G : government must regulate it
S : people will suffer
U : government will be unpopular

"If either wages or prices are raised, there will be inflation" : (W+P)->I ...(1)
"If there is inflation, then either the government must regulate it or the people will suffer" : I->(G+S)  ...(2)
"If the people suffer, the government will be unpopular" : S->U  ...(3)
"Government will not be unpopular" : U'  ...(4)

options are :
A. "People will not suffer" : S'
B. "If the inflation is not regulated, then wages are not raised" : I'->W'
C. "Prices are not raised" : P'
D. "If the inflation is not regulated, then the prices are not raised" : I'->P'
E. "Wages are not raised" : W'

using (3) and (4) we get
S' ...(5)
which is option A so option A is Valid
from (1), we do contrapositive of it 
I'->(W+P)' = I'->(W'.P')= (I'->W').(I'->P') which is options B and D respectively so options B and D are also valid 

Hence options A, B and D are valid 
 

2 votes
2 votes
  • $P:$ Wages are raised
  • $Q:$ Prices are raised
  • $R:$ There will be inflation
  • $T:$ The government must regulate it 
  • $U:$ The people will suffer
  • $V:$  The government will be unpopular

 

$1)\left ( P\vee Q \right )\rightarrow R$

$2)R\rightarrow \left ( T\vee U \right )$

$3)U\rightarrow V$

$4)\sim V$

 

From $(1)$ and $(2)$ we get

$\left ( P\vee Q \right )\rightarrow \left ( T\vee U \right )..............(5)$   [Hypothetical Syllogism]

 

Now we know from Modus Ponens

$U$

$U\rightarrow V$

--------------------------

          $V$

--------------------------

 

putting it in $(5)$ we get

$\left ( P\vee Q \right )\rightarrow \left ( T\vee V \right )........................(6)$

 

Now again with Disjunctive Syllogism

$\left ( P\vee Q \right )\rightarrow \left ( T\vee V \right )$

                          $\sim V$

---------------------------------------------------------

$\left ( P\vee Q \right )\rightarrow T$

 

i.e.If either wages or prices are raised,  the government must regulate it.

So, indirectly it tells $A)$ People will not suffer

Answer:

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