Triple integral - volume of solid described by inequalities

Question

I have to calculate the volume of solid described by inequalities: $$(x\leqslant y)\vee (y\leqslant z) \vee (x\leqslant z)$$ in region $[0,1]^3$. What is important, here we have conjunction. It is difficult for me to imagine this solid. However, I have an idea, but I am not sure if I am correct. I would be grateful, if somebody could give me hint or check my theory. So, negation of conditions above give us such inequalities: $$x>y \wedge y>z $$ Then, it is a pyramid with vertices in (0,0,0), (0,1,0), (0,1,1), (1,1,0) (in (x,y,z) coordinates). Volume of pyramid is as simple as it can be, in this case it is $1/6$. Since the volume of whole cube is 1, volume of first solid would be ${5}/{6}$. It is done without any integrals, but I am not sure if this solution is correct. The exercise was in set with other triple integrals.