Prove or disprove the following inference rules for functional dependencies. A proof can be made either by a proof argument or by using inference rules IR1
through IR3. A disproof should be done by demonstrating a relation instance that
satisfies the conditions and functional dependencies in the left hand side of the
inference rule but do not
satisfy the conditions or dependencies in the right hand side.
(a) {W ->Y, X ->Z} |= {WX ->Y }
(b) {X ->Y} and Z subset-of Y |= { X ->Z }
(c) { X ->Y, X ->W, WY ->Z} |= {X ->Z}
(d) {XY ->Z, Y ->W} |= {XW ->Z}
(e) {X ->Z, Y ->Z} |= {X ->Y}
(f) {X ->Y, XY ->Z} |= {X ->Z}

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2

explanation:

step-by-step explanation: