Question of the week came up in my schools logic club but there is not much information to it. Here is the question:
$$ \exists x\,[R(x)\wedge \lnot Q(x)],\ \forall x\,[P(x)\to Q(x)],\, \forall x[R(x)\to(P(x)\vee S(x))] \models \exists x\,[R(x)\wedge S(x)] $$ Describe in details all your work
Now I know that it does not want us to use formal deduction, so what method do they want us to use then? Formal Deduction is the only way I am familiar with at the moment but apparently that has been ruled out as a possible method.