If R is relation on a finite set A having n elements, then the number of reflexive relations on A is

a) 2^{n} b) 2^{n^2-n} c) 𝑛^{2} d) 𝑛^{n}

^{Kindly answer with full explanation. Thank you}

The function 𝑓:𝑅→𝑅 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 𝑓(𝑥)=2^{x}+2^{|x|} is a) one-one and onto b) many-one and onto c) one-one and into d) many-one and into

Please give full explanation. Thank you

If A and B have 𝑚 𝑎𝑛𝑑 𝑛 elements respectively, then the number of possible functions from A to B is

a) 𝑛𝑚 b) 𝑚𝑛 c) 𝑚𝑛 d) 𝑚+𝑛

𝐼𝑓 𝑓(𝑥)=2𝑥−1/𝑥+2, then 𝑓(1)𝑓^{-1}(−1)=

a) 0 b) 1 c) -1 d) 2

If 𝑓(𝑥) is a function such that 𝑓(𝑥+𝑦)=𝑓(𝑥) 𝑓(𝑦) 𝑎𝑛𝑑 𝑓(3)=125 𝑡ℎ𝑒𝑛 𝑓(𝑥)= a) 5 b) 𝑥^{5} c) 5𝑥 d) 5^{x}

^{Please give full explanation. Thank you}

The function 𝑓:𝑅→𝑅 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 𝑓(𝑥)=2𝑥+2|𝑥| is a) one-one and onto b) many-one and onto c) one-one and into d) many-one and into

If R is relation on a finite set A having n elements, then the number of reflexive relations on A is

a) 2

^{n}b) 2^{n^2-n}c) 𝑛^{2}d) 𝑛^{n}^{Kindly answer with full explanation. Thank you}The function 𝑓:𝑅→𝑅 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 𝑓(𝑥)=2

^{x}+2^{|x|}isa) one-one and onto b) many-one and onto

c) one-one and into d) many-one and into

Please give full explanation. Thank you

If A and B have 𝑚 𝑎𝑛𝑑 𝑛 elements respectively, then the number of possible functions from A to B is

a) 𝑛𝑚 b) 𝑚𝑛 c) 𝑚𝑛

d) 𝑚+𝑛

𝐼𝑓 𝑓(𝑥)=2𝑥−1/𝑥+2, then 𝑓(1)𝑓

^{-1}(−1)=a) 0 b) 1 c) -1 d) 2

If 𝑓(𝑥) is a function such that 𝑓(𝑥+𝑦)=𝑓(𝑥) 𝑓(𝑦) 𝑎𝑛𝑑 𝑓(3)=125 𝑡ℎ𝑒𝑛 𝑓(𝑥)=

a) 5 b) 𝑥

^{5}c) 5𝑥 d) 5^{x}^{Please give full explanation. Thank you}The function 𝑓:𝑅→𝑅 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑦 𝑓(𝑥)=2𝑥+2|𝑥| is

a) one-one and onto b) many-one and onto

c) one-one and into d) many-one and into

Please give full explanation. Thank you