Discrete Mathematics question

Question

Answer 1

(1)Upper bound of S1 = { 3 , 4 , 5 , 6 , 7 , 8 }

A lower bound of S1 =not Exists

Upper bound of S2 = { 6 , 7 , 8 }

Lower bound of S2 = { 1, 2, 3 }

(2)GLB(S1)=not Exists

LUB(S1)=3

GLB(S2)= 3

LUB(S2)=not Exist as both 6 and 7 are upper bounds and they are not related.

Comments

LUB(S1) is  3 ??

LUB(S2) is 3 ??

---

no both are wrong.

---

Reason plz

---

do you know what is LUB?

---

Not..actually... If u explain ..it will be beneficial to me..

---

make arrow in image 

for LUB = go for upward direction from that set and take 1st meeting point .

for GLB = go for lower direction from that set and take 1st meeting point .

---

@Anirudh. Plz guide me.

LUB(S₁)=3     I think because this is the first meeting pt of 1 and 2, right?

LUB(S₂)=6    I think because 3,4,5 meet here for the first time, right?

---

everything is fine but Lub of  s1 should be 3 as you considered the set of all upperbound of s1 here {3,4,5,6,7,8} then least upper bound of s1 should be 3

---

Why there is 3 in lower bound of S2={3,4,5}

---

LUB for S1 is 3 and LUB for S2 is 8 or not exist ?

---

LUB(S2) is not existing. Answer is edited.

Answer 2

S1 = {1, 2}

S2 = {3, 4, 5}

(i)

Upper Bound of S1 = {3, 4, 5, 6, 7, 8}

Lower Bound of S1 = Does Not Exist (Since there are no elements below them to Meet)

Upper Bound of S2 = {6, 7, 8}

Lower Bound of S2 = {1, 2, 3}

(ii)

GLB of S1 = Does Not Exist (Since there are no elements below them)

LUB of S1 = {3}

GLB of S2 = {3}

LUB of S2 = Does Not Exist (Since there is No Unique first Joining point)