But with these two covers x -> z and y -> z, we lost the relation between x and y.

Neither do we have x->y nor y->x

Neither do we have x->y nor y->x

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+2 votes

+4 votes

Miinimal (canonical) cover of a set of FDs is the minimal set of FDs such that all other FDs can be derived.

So, {X -> Y, Y -> Z, Z-> X}, {X->Z, Z-> Y, Y->X}

So, {X -> Y, Y -> Z, Z-> X}, {X->Z, Z-> Y, Y->X}

+1 vote

minimal cover is known as canonical cover

here two canonical cover are possible

we get canonical cover by eliminating redundant FDs

1st cv :

becoz z->x so we can replace x by z in y->xz ( becoz if child derivates sumthing dan child will surely do dat) nd get y->z (1)

by spliting we cn write x->yz as x->y (2) nd x->z(3)

if we combine (2) nd (1) by union rule we get x->z

which is nothing bt (3) FD so we cn elliminate (1) nd (2) becoz de r redundant

nd we got 1st canonical cover as {x->z}

similarly we got 2nd minimal cover as {y->z}.

see this:https://gateoverflow.in//blog/13/shortest-way-to-find-minimal-cover

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