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See attached picture.

The question asks to prove that the statement which I have written on the first line is true. But I somehow proceeded to proving it is false. Basically what I did was simplify the given expression into the form (P or Q) => R and said this is equivalent to (P=>R) ^ (Q=>R). Then just looking at P=>R I arrived at a contradiction, so because F^T if F, the entire initial proposition is false. Where am I going wrong..?

The question asks to prove that the statement which I have written on the first line is true. But I somehow proceeded to proving it is false. Basically what I did was simplify the given expression into the form (P or Q) => R and said this is equivalent to (P=>R) ^ (Q=>R). Then just looking at P=>R I arrived at a contradiction, so because F^T if F, the entire initial proposition is false. Where am I going wrong..?