Answerrr! three men are suspected of being double agents. when questioned by the authorities, they speak as follows: jackson: “max is a mole.” max: “gregory is a mole.” gregory: “max is lying.” assuming that moles like, other agents tell the truth, and there is just on mole among the three, determine: who is the mole? if, on the other hand there are two moles present, who are they?

There are two ways to look at this:

If someone is a mole, negate their proposition:

Jackson(mole) "Max is not a mole"
Max(mole) "Gregory is not a mole"
Gregory(mole) "Max is not lying"

Looking at it this way their are two options, either Max is a mole, or Jackson and Gregory are both moles.

To find out for certainty, we must go at a maximum with no contradictions, meaning one agent and two moles:

Jackson(mole) "Max is a mole"
Max(mole) "Gregory is a mole"
Gregory(agent) "Max is lying"

This is a contradiction because if Gregory is telling the truth, and Jackson is lying, then Gregory and Max are not moles

Jackson(mole) "Max is a mole"
Max(agent) "Gregory is a mole"
Gregory(mole) "Max is lying"

This works because if Jackson and Gregory are both moles, then Max is telling the truth and is not a mole, and Max states Gregory is a mole which is again true

Jackson(agent) "Max is a mole"
Max(mole) "Gregory is a mole"
Gregory(mole) "Max is lying"

This is also a contradiction since Max says Gregory is a mole, and in this case he is, Max would be telling the truth, but to our knowledge the moles are lying.

Therefore Jackson and Gregory are moles

Aand b are correctly balanced reactions. they have the same number of atoms in both sides of the reaction