Question
Prove that the following arguments are standard by constructing metaphorical proof
$(W\ O\ \rightarrow\ T)\ \&\ (F\ \rightarrow\ Y)$
$B\ \&\ (P\ \rightarrow\ W)$
$(E\ \rightarrow\ F)\ \&\ (H\ v\ I)$
$P\ v\ E$
$\therefore\ B\ \&\ (T\ v\ Y)$

Answer

$(1)\ (W\  \rightarrow\ T)\ \&\ (F\  \rightarrow\ Y)$ $P$
$(2)\ B\ \&\ (P\  \rightarrow\ W)$ $P$
$(3)\ (E\ \rightarrow\ F)\ \&\ (H\ v\ l)$ $P$
$(4)\ P\ v\ E$ $P/ \therefore\  B\ \&\ (T\ v\ Y)$
$(5)\ B$ $2,$ Simp.
$(6)\ E\  \rightarrow\ F$ $3,$ Simp.
$(7)\ P\  \rightarrow\ W$ $2,$ Simp.
$(8)\ W\  \rightarrow\ T$ $1,$ Simp.
$(9)\ F\  \rightarrow\ Y$ $1,$ Simp.
$(10)\ W\ v\ F$ $7, 6, 4, CD$
$(11)\ T\ v\ Y$ $8, 9, 10, CD$
$(12)\ B\ \&\ (T\ v\ Y)$ $5, 11,$ Conj.

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