URGENT Symbolize the following argument (using the given symbolization key); sho

Question

URGENT

Symbolize the following argument (using the given symbolization key); show that the argument is invalid by assigning truth values to these atomic parts:

if the government intervenes and there is no break in hostilities, then either there is a break in hostilities or Eritrea will suffer if, but only if, there is no government intervention. the only three possibilities are that either there is a break in hostilities, Eritrea suffers, or there will be no government interventions. So Eritrea will not suffer if and only if there is a break in hostilities.

I: the government intervenes B:there is a break in hostilities S: eritrea suffers

Thank you for your time

Explanation / Answer

I: the government intervenes
B: there is a break in hostilities
S: eritrea suffers

The first statement is,

if the government intervenes and there is no break in hostilities, then either there is a break in hostilities or Eritrea will suffer if, but only if, there is no government intervention.

This will be symbolized as,   (I &~B)->(B+(S<->~A))

The second statement is

the only three possibilities are that either there is a break in hostilities, Eritrea suffers, or there will be no government interventions.

This will be symbolized as, B+S+~I

The third statement is,

So Eritrea will not suffer if and only if there is a break in hostilities.
This will be symbolized as,  ~S<->B

If these three symbolized functions will be written one at a time, the truth values are attained but when they are combined, the combintion shows that the argument is invalid

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