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Best answer

There are three Ck : A, BC, CDE

**Take Each CK alone**

No. of superkeys when CK is A alone = 2^{4 }(Because each remaining 4 values may or may not be in the SK, hence 2 posibilities for each)

No. of superkeys when CK is BC alone = 2^{3 }(Because each remaining 3 values may or may not be in the SK, hence 2 posibilities for each)

No. of superkeys when CK is CDE alone = 2^{2 }(Because each remaining 2 values may or may not be in the SK, hence 2 posibilities for each)

**Now, take combinations from given CK**

No. of superkeys when CK is ABC = 2^{2 }(Because each remaining 2 values may or may not be in the SK, hence 2 posibilities for each)

No. of superkeys when CK is BCDE = 2^{1 }(Because each remaining 2 values may or may not be in the SK, hence 2 posibilities for each)

No. of superkeys when CK is ACDE = 2^{1 }(Because each remaining 2 values may or may not be in the SK, hence 2 posibilities for each)

**Now, take all three CK together**

No. of superkeys when CK is ABCDE = 2^{0 }(Because each remaining 2 values may or may not be in the SK, hence 2 posibilities for each)

Hence total SK = 2^{4} + 2^{3} + 2^{2} - 2^{2} - 2^{1} - 2^{1} + 2^{0 }= 16 + 8 + 4 - (4+2+2) + 1 = 28 - 8 + 1 = 21

**Hence total super keys are 21**