QUESTION 7 Consider the poset (A, R) represented by the following Hasse diagram (2 (a) Give each of the following If any do not exıst, explan why (i) The greatest element of (A, R) (i:) The least ele...
QUESTION 7 Consider the poset (A, R) represented by the following Hasse diagram (2 (a) Give each of the following If any do not exıst, explan why (i) The greatest element of (A, R) (i:) The least element of (A, R) (i) All upper bounds of {h, eh (iv) The least upper bound (LUB) or(h (v) All lower bounds of (b,c) (vi) The greatest lower bound (GLB) or(b, c} (b) Give complete reasons for the answers to the following (i) Is (A, R) a lattice? (n) A complement of c (i) A complement of d (iv) Is (A, R) a complemented lattice? (v) Is (A, R) a Boolean algebra? 16]
QUESTION 7 Consider the poset (A, R) represented by the following Hasse diagram (2 (a) Give each of the following If any do not exıst, explan why (i) The greatest element of (A, R) (i:) The least element of (A, R) (i) All upper bounds of {h, eh (iv) The least upper bound (LUB) or(h (v) All lower bounds of (b,c) (vi) The greatest lower bound (GLB) or(b, c} (b) Give complete reasons for the answers to the following (i) Is (A, R) a lattice? (n) A complement of c (i) A complement of d (iv) Is (A, R) a complemented lattice? (v) Is (A, R) a Boolean algebra? 16]