Let P - a- b- c- Q- g- h- x- y and R- a- e- f- s- Find the following- i P - R ii Q- R iii R- P- Q

(i) P $Rimplies elements inPthat are not inR.∴ P/R=b,c(ii) Q∩ Rimplies elements that are both inQandR ∴ Q∩ R=ϕ (Since no element is common for them). ...

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Byju's Answer

Standard XII

Mathematics

De Morgan's Law

Let P = a, b,...

Question

Let P ={ a, b, c}, Q={ g, h, x, y} and R= { a, e, f, s}. Find the following:
(i) $P ∖ R$ (ii) $Q \cap R$ (iii) $R ∖ (P \cap Q)$

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Solution

$(i) P$ \ $R$ implies elements in $P$ that are not in $R$ .
$∴ P$ / $R =$ { $b, c$ }
$(i i) Q \cap R$ implies elements that are both in $Q$ and $R$
$∴ Q \cap R =$ { $ϕ$ } (Since no element is common for them).
$(i i i) P \cap Q =$ { $ϕ$ }
$∴ R$ \ $(P \cap Q) =$ { $a, e, f, s$ }

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Let P ={ a, b, c}, Q={ g, h, x, y} and R= { a, e, f, s}. Find the following: (i) P∖R (ii) Q∩R (iii) R∖(P∩Q)

(i) P\R implies elements in P that are not in R.∴P/R={b,c}(ii) Q∩R implies elements that are both in Q and R∴Q∩R={ϕ} (Since no element is common for them).(iii)P∩Q={ϕ}∴R\(P∩Q)={a,e,f,s}

Let P ={ a, b, c}, Q={ g, h, x, y} and R= { a, e, f, s}. Find the following:
(i) $P ∖ R$ (ii) $Q \cap R$ (iii) $R ∖ (P \cap Q)$

$(i) P$ \ $R$ implies elements in $P$ that are not in $R$ .
$∴ P$ / $R =$ { $b, c$ }
$(i i) Q \cap R$ implies elements that are both in $Q$ and $R$
$∴ Q \cap R =$ { $ϕ$ } (Since no element is common for them).
$(i i i) P \cap Q =$ { $ϕ$ }
$∴ R$ \ $(P \cap Q) =$ { $a, e, f, s$ }