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Question 31 of 40

Q.Using the truth table, verify.
p∨(q∧r)≡(p∨q)∧(p∨r)p \vee (q \wedge r) \equiv (p \vee q) \wedge (p \vee r)

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2025Subjective· 4mImportance★★★★★
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A truth table over p,q,rp,q,r shows the columns of p∨(q∧r)p\vee(q\wedge r) and (p∨q)∧(p∨r)(p\vee q)\wedge(p\vee r) agreeing in every one of the 88 rows, proving the equivalence (the distributive law of ∨\vee over ∧\wedge).

We evaluate both sides for all 88 combinations. (T = true, F = false.)

ppqqrrq∧rq\wedge rp∨(q∧r)p\vee(q\wedge r)p∨qp\vee qp∨rp\vee r(p∨q)∧(p∨r)(p\vee q)\wedge(p\vee r)
TTTTTTTT
TTFFTTTT
TFTFTTTT
TFFFTTTT
FTTTTTTT
FTFFFTFF
FFTFFFTF
FFFFFFFF
…

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