I have a problem in proving invalid the following argument:
Horses and cows are mammals.Some animals are mammals.Some animals are not mammals.Therefore all horses are animals.
If we translate it into the logical notation then we have :
The premises are :
$(\forall x)(Hx \lor Cx \rightarrow Mx)$.
$(\exists x)(Ax \land Mx)$
$(\exists x)(Ax \land \sim Mx)$
The conclusion is :
$(\forall x)(Hx \rightarrow Ax)$.
Where $Ax$ is means $x$ is an animal, $Hx$ means $x$ is a horse, $Cx$ means $x$ is a cow, $Mx$ means $x$ is a Mammal.
I have to show it is an invalid argument.But the 2nd and 3rd premises are like contradictory to the conclusion part.
As per I know if I can show a truthvalue assignment for which the conclusion is false still the premises are true,then the argument will be invalid. But I am unable to find such a truthvalue assignment, looking for a help. Thanks.