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Miscellaneous Exercise 1 · Q162

Q.Construct the truth table for: [(p∧q)∨r]∧[∼r∨(p∧q)][(p \wedge q) \vee r] \wedge [\sim r \vee (p \wedge q)]

Maharashtra MsbshseTextbookSubjectiveImportance★★★★★
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Build the 8-row table over p,q,rp,q,r for [(p∧q)∨r]∧[∼r∨(p∧q)][(p\wedge q)\vee r]\wedge[\sim r\vee(p\wedge q)]:

p=T,q=T,r=Tp{=}T,q{=}T,r{=}T: p∧q=Tp\wedge q=T; (p∧q)∨r=T(p\wedge q)\vee r=T; ∼r∨(p∧q)=F∨T=T\sim r\vee(p\wedge q)=F\vee T=T; AND=T=T.

p=T,q=T,r=Fp{=}T,q{=}T,r{=}F: p∧q=Tp\wedge q=T; first bracket=T∨F=T=T\vee F=T; second=T∨T=T=T\vee T=T; AND=T=T.

p=T,q=F,r=Tp{=}T,q{=}F,r{=}T: p∧q=Fp\wedge q=F; first=F∨T=T=F\vee T=T; second=F∨F=F=F\vee F=F; AND=F=F.

p=T,q=F,r=Fp{=}T,q{=}F,r{=}F: p∧q=Fp\wedge q=F; first=F∨F=F=F\vee F=F; AND=F=F.

p=F,q=T,r=Tp{=}F,q{=}T,r{=}T: p∧q=Fp\wedge q=F; first=F∨T=T=F\vee T=T; second=F∨F=F=F\vee F=F; AND=F=F.

p=F,q=T,r=Fp{=}F,q{=}T,r{=}F: p∧q=Fp\wedge q=F; first=F∨F=F=F\vee F=F; AND=F=F.

p=F,q=F,r=Tp{=}F,q{=}F,r{=}T: p∧q=Fp\wedge q=F; first=F∨T=T=F\vee T=T; second=F∨F=F=F\vee F=F; AND=F=F.

p=F,q=F,r=Fp{=}F,q{=}F,r{=}F: p∧q=Fp\wedge q=F; first=F∨F=F=F\vee F=F; AND=F=F. …

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