Choosing pulldown resistor for 74LS86
Inputs on bipolar TTL (plain 74xx, 74LSxx, 74ALSxx, 74 anything without a "C") all source current, and must be pulled below 0.8 volts to be seen as a low.

Common practice for switch inputs was to put the switch between the input pin and ground, with a 5K or so resistor to +5V to ensure the input would really be seen as a High when the switch was open.

CMOS parts (anything with a "C" in the middle letters) have a very high input impedance, so can be used with a 5 - 10K pull-up resistor with a switch to ground, or 5 - 10K pull-down resistor, with a switch to +5V.