If R is relation on a finite set A having n elements, then the number of reflexive relations on A is
a) 2n b) 2n^2-n c) 𝑛2 d) 𝑛n
Kindly answer with 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
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) 𝑥5 c) 5𝑥 d) 5x
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) 2n b) 2n^2-n c) 𝑛2 d) 𝑛n
Kindly answer with 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
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) 𝑥5 c) 5𝑥 d) 5x
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