Question

State whether the given pairs of sets are equal or equivalent.
(i) $A=\left\{firstfournaturalnumbers\right\}$ and $B=\left\{firstfourwholenumbers\right\}$.
(ii) $A$ = Set of letters of the word $"FOLLOW"$ and $B$ = Set of letters of the word $"WOLF"$.
(iii) $E=\left\{evennaturalnumberslessthan10\right\}$ and $O=\left\{oddnaturalnumberslessthan9\right\}$
(iv) $A=\left\{daysoftheweekstartingwithletterS\right\}$ and $B=\left\{daysoftheweekstartingwithletterT\right\}$.
(v) $M=\left\{multiplesof2and3between10and20\right\}$ and $N=\{multiplesof2and5between10and,20\}$.
(vi) $P=\left\{primenumberswhichdivide70exactly\right\}$ and $Q=\left\{primenumberswhichdivide105exactly\right\}$.
(vii) $A=\{0^2,1^2,2^2,3^2,4^2\}$ and $B=\{16,9,4,1,0\}$.
(viii) $E=\{8,10,12,14,16\}$ and $F=\left\{evennaturalnumbersbetween6and18\right\}$.
(ix) $A=\left\{lettersofthewordSUPERSTITION\right\}$ and $B=\left\{lettersofthewordJURISDICTION\right\}$.

Answer 1

(i) $A=\left\{firstfournaturalnumbers\right\}=\{1,2,3,4\}$
$B=\left\{firstfourwholenumbers\right\}=\{0,1,2,3\}$.
It is an equivalent set as both have equal number of elements which are not same.

(ii) $A$ = Set of letters of the word $"FOLLOW"=\{F,0,L,W\}$
$B$ = Set of letters of the word $"WOLF"=\{W,O,L,F\}$.
It is an equal set as both have same and equal elements.

(iii) $E=\left\{evennaturalnumberslessthan10\right\}=\{2,4,6,8\}$
$O=\left\{oddnaturalnumberslessthan9\right\}=\{1,3,5,7\}$
It is an equivalent set as both have equal number of elements which are not same.

(iv) $A=\left\{daysoftheweekstartingwithletterS\right\}=\{Sunday,Saturday\}$
$B=\left\{daysoftheweekstartingwithletterT\right\}=\{Tuesday,Thursday\}$.
It is an equivalent set as both have equal number of elements which are not same.

(v) $M=\left\{multiplesof2and3between10and20\right\}=\{12,14,15,16,18\}$
$N=\{multiplesof2and5between10and,20\}=\{12,14,15,16,18\}$.
It is an equal set as both have same and equal elements.

(vi) $P=\left\{primenumberswhichdivide70exactly\right\}=\{2,5,7\}$
$Q=\left\{primenumberswhichdivide105exactly\right\}=\{3,5,7\}$.
It is an equivalent set as both have equal number of elements which are not same.

(vii) $A=\{0^2,1^2,2^2,3^2,4^2\}=\{0,1,4,9,16\}$
$B=\{16,9,4,1,0\}$.
It is an equal set as both have same and equal elements.

(viii) $E=\{8,10,12,14,16\}$
$F=\left\{evennaturalnumbersbetween6and18\right\}=\{8,10,12,14,16\}$.
It is an equal set as both have same and equal elements.

(ix) $A=\left\{lettersofthewordSUPERSTITION\right\}=\{S,U,P,E,R,T,I,O,N\}$
$B=\left\{lettersofthewordJURISDICTION\right\}=\{J,U,R,I,S,D,C,T,O,N\}$.
It is neither equal nor equivalent sets as they have different and unequal elements.