The Boolean expression (X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to

Consider the Boolean function, F(w,z,y,z)=wy+ xy +$$\overline w \,xyz + \overline w \,\overline x y\, + xz + \,\overline {x\,} \,\overline y \,$$ $$\overline z $$ Which one of the following is the complete set of essential prime implicants?

The output F in the digital logic circuit shown in the figure is

Five JK flip - flops are cascaded to form circuit shown in figure. Clock pulses at a frequency of 1 MHz are applied as shown. The frequency (in kHz) of the waveform at Q₃ is ______.