Consider the following premises: (1) Mixing of compounds A and B causes an explo

Question

Consider the following premises: (1) Mixing of compounds A and B causes an explosion if and only if both compounds are in gas form 2) Compound A exists in gas form only if the room temperature is at least (3) Compound B cannot exist in gas form if the pressure in the room is under 4) The room where I am performing chemical experiments has a temperature (a) 1] Write each of the premises in sym 30o C. 0.5 atmosphere. of 25° C and a pressure of 0.3 atmosphere mbolic form (b) 2 Give a logical argument, using the rules of inference, that shows that the following conclusion is justified: In the room where I am performing chemical experiments, compound A and B can be mixed without causing an explosion. Give a counterexample to show that the following conclusion does NOT follow from premises (1), (2) and (3) If compounds A and B are mixed together and do not cause an explosion, then the room temperature is below 30 or the room pressure is at least 0.5 atmosphere. (c

Explanation / Answer

(a) and (b)

Let

Mixing of A and B : M

Explosion on missing : E

A being in gas form : A

B being in gas form : B

Room temperature is at least 30 : T

Room pressure is higher than 0.5 atmosphere unit : P

Given

1

A & B & M => E

2

~T => ~A

3

~P => ~B

4

T = false

P = false

from 4 and 2: A = false

from 4 and 3: B = false

As A and B are false, A & B & M is false so no explosion

(c)

Given E = false

so A & B & M = false

M = true

so A&B = false

A is false or B is false.

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