If you cover one of the slits in the double-slit experiment and record the resulting pattern, and then repeat the experiment with the other slit covered and record that pattern as well, the sum of the two patterns will not be the same as the pattern obtained when both slits are open simultaneously. This is because the interference pattern observed in the double-slit experiment is a result of the superposition of wavefunctions from both slits.
When both slits are open, the waves associated with each slit interfere with each other, leading to an interference pattern on the screen. This pattern exhibits alternating regions of bright and dark fringes due to constructive and destructive interference. The combined pattern arises from the interference between the wavefronts passing through both slits.
However, if you cover one slit and record the pattern, the resulting pattern will resemble that of a single-slit diffraction, where the wave passes through a single opening and spreads out. It will exhibit a central bright fringe with progressively dimmer fringes on either side.
Summing up the patterns obtained by covering each slit separately will not recreate the interference pattern observed when both slits are open because the interference between the waves from the two slits is missing. The superposition of the wavefunctions from both slits is necessary to generate the characteristic interference pattern.