$($a$)$ Use the method of conditional proof to verify that the following is a tautology $($PQ$)-1-($QR$)$~$($R$-$P

Attempted $0/1$

$(2$ marks$)$

$($b$)$ Use the strengthened method of conditional proof to prove the validity of the following

$366$argument: $($PvQ$)($Rv$5157$marks$)$

$($c$)$ Symbolize the following argument by using the suggested notations: $"$If Arun joins the alliance, then either Bhaskar or Chander will boycott it$.$ If Bhaskar boycotts the Stt alliance

then Charider will boycott it also. Therefore, if Arun joins the alliance, then Chander will boycott it$."$

Use the following notations:

OGEA: "Arun joins the alliance."

B: "Bhaskar boycotts the alliance."

C: "Chander boycotts the alliance."

VY$(2$ marks$)$

$($d$)$ Prove the validity of the following argument by using quantification theory: "All houses built of brick are warm. Some houses in Chennai are built of brick. Therefore some Dhouses

in Chennai are warm." Use the following notations:

Hx: $\text{'}$x is a house.$\text{'}$;

Bx: $\text{'}$x is built of brick.$\text{'}$

Wx: $\text{'}$x is warm.$\text{'}$;

Cx: x is in Chennai.