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Venn Diagram

Express the t...

Question

Express the truth of each of the following statements using Venn diagrams.
(1) All teachers are scholars and scholars are teachers.
(2) If a quadrilateral is a rhombus then it is a parallelogram

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Solution

a.) Fig. 1
$H =$ Set of all humans
$T =$ set of all teachers
$S =$ set of all scholars
All teachers are scholars and all scholars are teachers. So, truth value $T = S$
b) If a quadrilateral is a rhombus them it is a parallelogram
(Fig. 2)
$R =$ set of rhombus
$P =$ Set of parallelogram
$Q =$ Set of quadrilaterals
$∴$ R is a subset of P

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